Question

An investment will provide you with $100 at the end of each year for the next 10 years. What is the present value of that annuity if the discount rate is 8% annually? What is the present value of the above if the payments are received at the beginning of each year? If you deposit those payments into an account earning 8%, what will the future value be in 10 years? What will the future value be if you open the account with $1,000 today, and then make the $100 deposits at the end of each year?

Answer 1

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

=$100[1-(1.08)^-10]/0.08

=$100*6.710081399

=$671.01(Approx).

b.

Present value of annuity due=Present value of annuity*(1+interest rate)

=$671.01*1.08

=$724.69(Approx)

c.

Assuming end of year payments:

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

=$100[(1.08)^10-1]/0.08

=$100*14.48656247

=$1448.66(Approx)

[If future value is required for beginning of year payments;future value would be=$1448.66*1.08

=$1564.55(Approx).]

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

A for $1000=$1000(1.08)^10

Hence total future value

=$1000(1.08)^10+1448.66

=(1000*2.158924997)+1448.66

=$3607.58(Approx).