Question

1. What is the present value of $3,570 to be received at the beginning of each of 27 periods, discounted at 5% compound interest?

2. What is the future value of 15 deposits of $2,580 each made at the beginning of each period and compounded at 10%?

3. What is the present value of 9 receipts of $3,010 each received at the beginning of each period, discounted at 9% compounded interest?

Answer 1

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

1.Present value=3570+3570/1.05+3570/1.05^2+...........+3570/1.05^26

=3570[1+1/1.05+1/1.05^2+...........+1/1.05^26]

=3570*15.3751853

which is equal to

=$54889.41(Approx)

2.

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=2580(1.1)^15+2580(1.1)^14+2580(1.1)^13+..........+2580(1.1)^1

=2580[(1.1)^15+(1.1)^14+..........+(1.1)^1]

=2580*34.94972986

=$90170.30(Approx)

3.

Present value=3010+3010/1.09+3010/1.09^2+............+3010/1.09^8

=3010[1+1/1.09+1/1.09^2+............+1/1.09^8]

=3010*6.534819115

which is equal to

=$19669.81(Approx).