Business Mathematics Brief 12th Edition by Stanley Salzman ,Gary Clendenen, Charles Miller

Exercise 145

Find the amount of this annuities due rounded to the nearest cent. Find the total interest earned. (See Example.) Describe the differences between an IRA, a 401(k), and a 403(b). (See Objective.)
Finding the Amount of an Annuity Due
Quick TIP
For an annuity due, be sure to add 1 period to the number of compounding periods and subtract 1 payment from the amount calculated.
Mr. and Mrs. Thompson set up an investment program using an annuity due with payments of $500 at the beginning of each quarter. Find (a) the amount of the annuity and (b) the interest if they make payments for 7 years into an investment expected to pay 8% compounded quarterly.
SOLUTION
(a) Step 1 Interest of
is earned each quarter. There are 7 × 4 = 28 periods in 7 years. Since it is an annuity due, add 1 period to 28, making 29 periods.
Step 2 Look across the top of the table for 2% and down the side for 29 periods to find 38.79223.
$500 × 38.79223 = $19,396.12 (rounded)
Step 3 Now subtract one payment to find the amount of the annuity due.
Amount of annuity due = $19,396.12 ? $ 500 = $18,896.12
(b) Subtract the 28 payments (7 years × 4 payments per year) of $500 each to find the interest.
Interest = $18,896.12 ? 1 28 × $500 2 = $ 4896.12
The calculator solution to finding the interest in part (b) follows.

Note: Refer to Appendix B for calculator basics.