Question

a. What is the future value of $10,000 invested for 15 years at 9%?

b. What is th future value of $10,000 invested each year for 15 years at 9%?

c. What amount must be invested today to pay out the following if 8% can be earned on investments?

-$10,000 in 10 years

-$10,000 in each of the next 10 years

Answer 1

a.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=$10000(1.09)^15

=$10000*3.64248246

=$36424.82

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

$10000[(1.09)^15-1]/0.09

=$10000*29.36091622

=$293,609.16(Approx).

c.Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period

$10000/1.08^10

=$10000*0.463193488

=$4631.93(Approx).

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

=$10000[1-(1.08)^-10]/0.08

$10000*6.710081399

=$67100.81(Approx).