Question

You want to have $47,000 in your savings account 9 years from now, and you're prepared to make equal annual deposits into the account at the end of each year. If the account pays 7.1 percent interest, what amount must you deposit each year?

Answer 1

Amount to be deposited each year = $3,907.58

Step-by-step explanation:

The equal annual deposit can be worked out using the future value of an ordinary annuity formula. An an annuity is a series of equal cash flows receivable for certain number years.

Future Value of an ordinary annuity (FVOA). The represents the total sum of that would accrue where a series of annual cash flow (each occurring at the end of the year) is compounded at a particular rate. It can be determined as:

A=FV ÷( (1+r)^n - 1)/r).

FV- Future value

A- annual cash flow

R- rate of interest

n-number of years

The first cash flow does earn interest in the first year because it occurs at the end of the year

( (1+r)^n - 1)/r)= (1.071^9 - 1)/0.071=12.028

FV- 47,000

A= 47,000/12.028 = 3907.58

A-$3,907.58

Amount to be deposited each year = $3,907.58