Question

Cindy Medavoy will invest $6,250 a year for 22 years in a fund that will earn 15% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 22 years? If the first payment occurs at year-end, what amount will be in the fund in 22 years?

First payment today?

First payment at year-end

Answer 1

If first payment is made today the series of payments is called annuity due.

If firstpayment is made at the year end the series of payment is called ordinary annuity.

now,

The amount of fund in 22 years if first payment is made today can be calculated from the below mentioned formula:

=>(1+r) * P[(1+r)^n - 1] /r

here,

r = 15% =>0.15.

n =22 years.

P = $6250.

n = 22 .

=> future value of annuity due = (1.15) *$6250[(1.15)^22 - 1] / 0.15

=> (1.15) *$6250 [ 20.6447457 / 0.15]

=>1.15 * $6250 * 137.631638.

=>$989,227.40...(rounded to two decimals).

Future value if first payment is made today = $989,227.40.

NOw,

If the first payment is made at the year end.

future value of annuity = A * [(1+r)^n - 1] /r

=>$6,250 * [(1.15)^22 - 1] / 0.15

=>$6,250 * [20.6447457/0.15]

=>6250*137.631638.

=>$860,197.74...(rounded to two decimals).

Future value if payment is made at year end = $860,197.74.