Question

You want to have $68,000 in your savings account 5 years from now, and you're prepared to make equal annual deposits into the account at the end of each year.

Required:

If the account pays 7.3 percent interest, what amount must you deposit each year?

Answer 1

Since the deposits are to be made each year with equal amounts, so it will be an annuity. And the deposits will be made at year end, so it will be ordinary annuity.We have to use the formula for future value of ordinary annuity. The formula for future value of ordinary annuity is :

Future value of ordinary annuity = P * ((1 + r)ⁿ - 1) / r),

where, P is the periodic deposits, r is the rate of interest = 7.3% and n is the time period = 5

Now, putting these values in the above formula, we get,

$68000 = P * ((1 + 7.3%)⁵ - 1) / 7.3%)

$68000 = P * ((1 + 0.073)⁵ - 1) / 0.073)

$68000 = P * ((1.073)⁵ - 1) / 0.073)

$68000 = P * ((1.42232423428 - 1) / 0.073)

$68000 = P * (0.42232423428 / 0.073)

$68000 = P * 5.78526348324

P = $68000 / 5.78526348324

P = $11754

So, annual deposits are $11754 each year