Question

You wish to deposit an amount now that will accumulate to $100,000 in 10 years. How much less would you have to deposit if the rate of interest was 8% compounded monthly versus annually?

Answer 1

For monthly:

We use the formula:
A=P(1+r/12)^12n
where
A=future value
P=present value
r=rate of interest
n=time period.

100,000=P*(1+0.08/12)^(12*10)

P=100,000/(1+0.08/12)^(12*10)

=100,000*0.450523461

=$45052.35(Approx)

For annual deposit:

We use the formula:
A=P(1+r/100)^n
where
A=future value
P=present value
r=rate of interest
n=time period.

100,000=P*(1.08)^10

P=100,000/(1.08)^10

=100,000*0.463193488

=$46319.35(Approx)

Hence less deposit to be made=46319.35-45052.35

=$1267(Approx).