Question

Find the future values of the following ordinary annuities: FV of $600 paid each 6 months for 5 years at a nominal rate of 10% compounded semiannually. Do not round intermediate calculations. Round your answer to the nearest cent.

FV of $300 paid each 3 months for 5 years at a nominal rate of 10% compounded quarterly. Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

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

1st case.

A=$600

r=10% per annum =>10%*6/12 =>5%

=>0.05

n = 5years * 2 six month periods each=>10

future value of annuity = $600*[(1.05)^10-1]/0.05

=>$600*12.5778926

=>$7,546.74.

2nd case.

A=$300

r=10% per year =>10%*3/12=>2.5% per quarter

=>0.025

n =5 years*4 quarters

=>20.

future value of annuity = $300*[(1.025)^20-1]/0.025

=>$300*25.5446576

=>$7,663.40.