Question

1. Derek will deposit $5,035.00 per year for 26.00 years into an account that earns 8.00%, The first deposit is made next year. How much will be in the account 37.00 years from today?

2. Derek will deposit $1,817.00 per year for 25.00 years into an account that earns 8.00%. The first deposit is made today. How much will be in the account 25.0 years from today?

Answer 1

1.Present value of annuity=Annuity[1-(1+interest rate)^-time period]/rate

=$5035[1-(1.08)^-26]/0.08

=$5035*10.80997795

=$54428.23898

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

Hence

A =$54428.23898*(1.08)^37

=$938,649.03(Approx).

b.Future value of annuity due=(1+rate)*Annuity[(1+rate)^time period-1]/rate

=1.08*1817[(1.08)^25-1]/0.08

=1817*78.95441515

=$143,460.17(Approx).