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12.4 Mathematics of Finance

Focus on future value of an annuity and monthly loan payment.

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Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Amount of an annuityWorked steps · five questions02Present value and installment paymentsWorked steps · five questions
Lesson brief and rules

12.4 Mathematics of Finance

For end-of-period payments RR, annuity future value is R[(1+r)n−1]rR\frac{[(1+r)^{n}-1]}{r} and present value is R[1−(1+r)−n]rR\frac{[1-(1+r)^{-n}]}{r}; rr is the rate per payment period.

Worked example 11
01 / Deposit $7575 at the end of each month for 22 years at 5%5\% per year compounded monthly. Find the future value, rounded to the nearest cent.
02 / There are n=24n = 24 deposits and the monthly rate is r=5%12r = \dfrac{5\%}{12}. Future value =75[(1+r)24−1]r== 75\dfrac{[(1 + r)^{24} - 1]}{r} = $1888.941888.94.
03 / Answer: $1888.941888.94
Worked example 2 · Monthly loan payment

A $60006000 loan is repaid by equal end-of-month payments over 33 years at 6%6\% per year compounded monthly. Find the monthly payment, rounded to the nearest cent.

Solve P=R[1−(1+r)−n]rP = R\dfrac{[1 - (1 + r)^{-n}]}{r} for RR. Here P=6000,r=0.0612P = 6000, r = \dfrac{0.06}{12} and n=36n = 36, so R=R = $182.53182.53. Answer: $182.53182.53

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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