Question

How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?

Answer 1

7606.62

Explanation:

Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.

`p(((1+i)^n-1)/(i))*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75((1+.0029166667)^(120)-1)/(.0029166667)*(1+.0029166667)= 10788.814149\\`

Now just equate this to a time 0 payment at the same rate

`10788.814149=(1+.0029166667)^(120)*x\\x= 7606.6228603=7606.62`

As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.