Practice Annuities in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A series of equal payments made at regular intervals over a fixed period of time. The future value and present value formulas calculate the total worth of these payment streams.

Imagine depositing \$100 every month into a savings account. Each deposit earns interest for a different amount of time—the first deposit earns interest for the full term, the last deposit barely earns any. An annuity formula adds up all these differently-growing deposits in one clean expression, instead of computing compound interest on each payment separately.

Showing a random 20 of 50 problems.

Example 1

hard
How many years until \$300 monthly deposits reach \$100,000 at 7.2% annual interest compounded monthly?

Example 2

easy
Present value: PMT=100PMT = 100, i=0.05i = 0.05, n=1n = 1.

Example 3

challenge
A loan is amortized with PMT=400PMT = 400, i=0.01i = 0.01 monthly, n=24n = 24. Find the original loan amount.

Example 4

medium
A loan of PV=1000PV = 1000 is repaid over n=2n=2 periods at i=0.10i = 0.10. Find the payment PMTPMT.

Example 5

easy
An ordinary annuity pays at the END of each period. What is paid at the BEGINNING called?

Example 6

easy
Find the present value of an ordinary annuity with PMT=$100PMT = \$100, i=0.05i = 0.05, n=2n = 2.

Example 7

medium
Find the monthly payment on a \$250,000 mortgage at 5.4% annual interest compounded monthly over 30 years.

Example 8

easy
A 20-year monthly annuity has how many payment periods nn?

Example 9

easy
How many payment periods nn does a 15-year monthly annuity have?

Example 10

hard
A 30-year mortgage of \$320,000 at 6% annual interest compounded monthly. How much total interest is paid?

Example 11

easy
For monthly payments at 6% annual interest, find the periodic rate ii.

Example 12

hard
Compare an ordinary annuity and an annuity due, both with $500\$500 monthly payments at 6%6\% annual interest compounded monthly for 55 years. How much more does the annuity due accumulate?

Example 13

challenge
Find the future value of an ordinary annuity with PMT=1000PMT=1000, annual rate 8% compounded quarterly, for 2 years.

Example 14

medium
How much more is an annuity due worth than an ordinary annuity with FVord=1000FV_{ord} = 1000 and i=0.08i = 0.08?

Example 15

medium
What is the future value formula when the periodic rate equals zero?

Example 16

medium
Identify the error: a student computes a mortgage payment using FV=PMT⋅(1+i)n−1iFV = PMT\cdot\frac{(1+i)^n-1}{i}. What should they use?

Example 17

easy
An annuity due is paid at the beginning of each period. Which formula multiplier converts an ordinary annuity FV to annuity-due FV?

Example 18

medium
Find the present value of an annuity: PMT=100PMT = 100, i=0.10i = 0.10, n=2n = 2.

Example 19

hard
If \$10,000 is invested today and \$200/month is added at the end of each month for 20 years at 6% annual interest compounded monthly, find the future value.

Example 20

medium
An annuity due pays \$400 at the start of each month for 3 years at 6% annual interest compounded monthly. Find the future value.
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