Question

You expect to receive a one-time payment of $1,000 in 10 years and the second payment of $1,500 in 15 years. The annual interest rate is 9%.

Part 1

What is the present value of the combined cash flows?

Part 2

If you invest the amount that you'll receive in 10 years and include the cash flow in year 15, how much money will you have in year 15?

Part 3

If you invest the amount found in part 1 for 10 years, how much will you have at the end?

Part 4

If you invest the amount found in part 3 for another 5 years, how much will you have at the end?

Answer 1

- You expect to receive a one-time payment of $1,000 in 10 years and the second payment of $1,500 in 15 years

Part 1) Calculating the Present value of combined cashflows:-

Present value of combined cashflows = [Payment in Year 10/(1+r)^10] + [Payment in Year 15/(1+r)^15]

where, r = Interest rate = 9%

Present value of combined cashflows = [$1,000/(1+0.09)^10] + [$1500/(1+0.09)^15]

= ($1000/2.36736367459) + ($1500/3.64248245969)

= $422.4108 + $411.8071

Present value of combined cashflows = $834.22

Part-2) Payment in year 10 = $1,000

Calculating its Future value in year end 15:-

Future Value = Payment*(1+r)^n

where, r = Interest rate = 9%

n = no of years = 5

Future Value = $1000*(1+0.09)^5

Future Value = $1000*1.5386239549

Future Value = $1538.62

- Total Future Value = Future Value + Payment in Year 15

Total Future Value = $1538.62 + $1500

Total Future Value = $3038.62

Part-3)

Present value today of Part 1 = $834.22

calculating its Future Value at the end of year 10:-

Future Value = Present value*(1+r)^n

where, r = Interest rate = 9%

n = no of years = 10

Future Value = $834.22*(1+0.09)^10

Future Value = $834.22*2.36736367459

Future Value = $1974.90

So, amount at the end of year 10 is $1974.90

Part-4)

Value at the end of year 10 = $1974.90

calculating its Future Value at the end of year 15:-

Future Value = Value at the end of year 10 *(1+r)^n

where, r = Interest rate = 9%

n = no of years = 5

Future Value = $1974.90*(1+0.09)^5

Future Value = $1974.90*1.5386239549

Future Value = $3038.62

So, amount at the end of year 15 is $3038.62