Question

Skylar plans to use $3400 to open a savings account with an annual interest rate of 1.15%. How much more interest will he earn over 13 years if he chooses a compound interest account that compounds interest quarterly instead annually? Round your answer to the nearest cent. interest compounded annually: A = P (1 + r)t interest compounded quarterly: A = P (1 +fraction numerator r over denominator 4 end fraction)4t

Answer 1

Given
Present investment, P = 3400
APR, r = 0.0115
compounding time = 13 years
Future amount, A 

A. compounded annually
n=13*1=13
i=r=0.0114
A=P(1+i)^n
=3400*(1+0.0115)^13
=3944.895

B. compounded quarterly
n=13*4=52
i=r/4=0.0115/4
A=P(1+i)^n
=3400*(1+0.0115/4)^52
=3947.415


Therefore, by compounding quarterly, he will get, at the end of 13 years investment, an additional amount of
3947.415-3944.895
=$2.52 (to the nearest cent)