Question

You invest $4970 at the beginning of every year and your friend invests $4970 at the end of every year. You both earn an annual rate of return of 14.00%.

a) How much will you have in your account after 11 years?

b) How much will your friend have in his account after 11 years?

Answer 1

a. The amount you will have in your account can be known using future value of annuity due;

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

here,

r =14%=>0.14

n=11

P=4970

=>(1.14)*4970*[(1.14)^11-1]/0.14

=>5665.80*[4.2262323-1]/0.14

=>5665.80*[23.04451644]

=>$130,565.62.

b. how much your friend will have in his account can be know using the future value of ordinary annuity;

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

here,

P=4970

r=14%.

n=11

amount in friend's account in 11 years = 4970*[(1.14)^11-1]/0.14

=>4970*23.0445164

=>$114,531.25.