Master Mathematics of The Time Value of Money

Explore simple interest, calculated on the principal using current value, rate, and time, with a $2,000 deposit at 3.5% for five years yielding $350.

Calculate the rate of simple interest using r = I/(P·n). Apply the example: a $1,500 principal over 3 years earned $236.25, yielding 5.25% per year.

Calculate term of maturity in simple interest using current value, interest earned, and rate of interest, via n = I / (CV × r), with a $3,000, 5.5% example.

Compute present value in the simple interest method by using current value, interest earned, rate, and time, and apply a practical example at 6% for four years.

Learn to calculate the future value using the simple interest method by applying the formula current value times (1 plus r times n) to grow the principal.

Learn to derive the term of maturity and the rate of interest from the future value formula using current value, future value, r, and n.

Explore deriving current value from future value via the simple discount method, where cv=fv/(1+r)^n, noting that simple discount equals interest.

Learn simple discount for a non-interest bearing future amount. Calculate its present value using current value = future value / (1 + R n) with 5500 due in eight months at 6.5%.

Apply simple discount to an interest-bearing future amount by calculating future value of $3,500 at 12% for ten months and discounting it at 14% to settle three months early.

Calculate loan term days using exact time and approximate time methods, subtracting serial day numbers for start and due dates to find the exact duration.

Learn the approximate time method using 30-day months and 360-day years to compute ordinary simple interest, compare with exact interest using 365 (or 366) days, and explore banker's rule.

Learn the relation between ordinary and exact simple interest in the time value of money, with Io = Ie × (1 + 1/72) and Ie = Io × (72/73).

Explore focal date and the equation of value to compare funds over time by discounting future payments to present value using simple interest, as shown in a Jimmy loan example.

Apply the focal date and equation of value to calculate Jill’s single payoff at 18 months under an 8.5% annual simple interest. Move the 5,500 forward to 18 months and discount the 6,750 back to the focal date, producing about 5,850.63 and 6,221.20, for a total of about 12,071.82.

Bring two loans to a common focal date using the given interest rate, apply future value and past value concepts, and sum to a single payment.

Apply focal date, equation of value to a $1,300 debt due in seven months, discount to $1,250 at three months, and project $1,365 at twelve months at 12% per annum.

Compute the average due date, or equated date, for multiple payments using a weighted average. Determine a single discharge date with interest.

Explore how partial payments affect loan balances under merchant's rule and US rule. See how focal date and interest adjustments discount principal.

Learn to compute the simple interest rate using the dollar-weighted method, given starting balance, deposits, withdrawals, and ending balance, with a step-by-step example yielding about 11.65% per year.

Explore bank discount and its distinction from simple discount and simple interest, where the discount rate applies to the future value to yield the proceeds.

Demonstrates bank discount mechanics by solving how proceeds and discount amount relate to future value, current value, discount rate, and term in a 1.5 year loan.

Discover how to compute the bank discount rate and discount term from current value and future value, using the bank discount formulas with practical examples.

Compare simple discount and bank discount by applying the same 9% annual rate to a $5,000 future value over six months, and compute current values and discounts.

Explore how interest rate and bank discount rate apply to discounting a promissory note. See a solved example where Brian discounts Michael's note to obtain cash and the bank's earnings.

Explore the time value of money by discounting a promissory note, calculating maturity and future value. The bearer receives $7,888.55, while the bank earns $313.47.

Explore how treasury bills are discounted to present value, with bid percentage and discount rate linked in the bank discount formula, for notes maturing within a year.

Explore discounting a treasury bill by solving a 182-day, $15,000 example with the traditional method and the D formula to compute the discount rate.

Demonstrate discounting a treasury bill by computing the purchase price from the bid percentage, then finding the discount amount and the discount rate for a 271-day five lakh bill.

Compare compound interest with simple interest, showing how interest on principal and prior interest grows the future value exponentially over three years.

Derive the compounding formula to compute future value from the current value using FV = CV(1+r)^n. Apply it to $12,000 at 7.33% for five years, yielding $17,094.15 and $5,094.15 interest.

Learn to compute present value from future value using the compound interest method, discounting with (1+r)^n, illustrated by a $5,000 inheritance at 6.75% for four years.

Explore how the current value of a $5,000 inheritance changes under three scenarios using compound interest and discounting, showing how rate and time affect the future value and current value.

Learn to find the interest rate using the compound interest method by solving r = nth root of future value over current value minus one, with a car example.

Derive the compounding term n from FV = CV(1 + r)^n using logs to isolate n, as shown with FV 13,000, CV 6,777, r 0.09375, yielding n about 7.27 years.

Explore the rule of 72 and rules 114 and 167 to estimate the time for current value to grow to future value, double, triple, or fivefold, at a given rate.

Explore how the effective interest rate differs from the nominal rate, driven by the conversion period and compounding frequency, with examples from annual to daily.

Explore types of compounding and how frequency affects interest yield and future value for a $1,000 investment at 7.25% over 3.5 years, from annual to daily and weekly.

Explore continuous compounding, its theoretical limit to e, the effective rate concept, and the future value formula, then compare with daily compounding through examples.

Learn how to use focal date and the equation of value with compound interest to compare funds at a common point in time, illustrated by a monthly-compounded example.

Compute the equated time and equated date for a loan with annual 5% compound interest by discounting installments to a focal present date and solving an equation of value.

Explore annuities as equal payments at equal intervals and distinguish ordinary annuity, annuity due, and deferred annuity by payment timing, term, and compounding, including perpetuity.

Explain the future value of an ordinary annuity (annuity immediate) with end-of-period payments, derive the FV formula, and show how to adjust for different compounding periods using an example.

Compute the future value of an ordinary annuity with semiannual compounding, using $600 semiannual contributions over 40 years at 6.25%, resulting in $205,922.11 and $157,922.11 in interest.

Compute the current value of an ordinary annuity by discounting each payment or by discounting the total future value, with monthly or quarterly compounding and conversion period.

Calculate the annuity payment from a future value using the ordinary annuity formula with rate, term, and conversion period m, featuring monthly or quarterly examples.

Learn to compute the annuity payment from a given current value for an ordinary annuity by rearranging the current-value formula using n, r, and m.

Learn to find the term of an ordinary annuity by rearranging the future value formula and applying logarithms, with a quarterly example of 6500 toward 60,000.

Find term n of an ordinary annuity by rearranging the current value formula and using logs. Example: a 230,000 deposit at 9.25% monthly compounding yields 57 months of 5,000 withdrawals.

Find the interest rate of an ordinary annuity by solving future value or current value formulas with the Newton-Raphson method; the method yields r for quarterly compounding (example: 7.9% annual).

Compute the interest rate for a bi-monthly ordinary annuity from the current value formula using Newton-Raphson, shown with a $10,500 fund and $250 payments, yielding about 7.52%.

Learn annuity due, where payments start each period, and compute its future and present values with monthly compounding. For example, $550 deposits over 5 years at 7% yield about $39,606.

Calculate the future value of weekly annuity due payments of $200 at the start of each week, using 2.5% annual interest compounded weekly over two years.

Compute the present value of an annuity due with monthly deposits of 750 for three years at 5.75 percent compounded monthly.

Calculate annuity payments for an annuity due using future value or current value with monthly compounding. Learn formulas and apply them to examples like installment purchases.

Derive the annuity due term using future value or current value, rearranging formulas and applying logarithms with monthly compounding and careful log bases, illustrated by mortgage examples.

Learn how a deferred annuity extends an ordinary payment by a deferment period before the first payment, with end of period payments and calculations of current and future value.

Calculate the current value of a $250 monthly deferred annuity with a three-month deferment under a 7% monthly compounded rate, spanning 18 payments from April 2008 to September 2009.

Calculate the future value of a deferred annuity using the ordinary annuity formula. Work through a quarterly $500 payment over two years with deferment and 8% interest.

Compute the current value of a deferred annuity using the formula, applying it to a $500 quarterly payment over two years with a one-quarter deferment at 8%.

Explore perpetuity, an infinite annuity, and learn to compute perpetuity payments using current value, interest rate, and conversion period. See a seven lakh 50,000 scholarship example that yields 80,625.

Master the perpetuity concept through solved examples, including semiannual compounding, calculating present value from annuity payments and determining required interest rates.