Question

Assume you are to receive a 10‐year annuity with annual payments of $1000. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will invest each payment in an account that pays 9 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not withdraw any money from the account until 25 years from today, and the account will continue to earn 9% for the entire 25‐year period. What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)?

Answer 1

The value in your account at the end of Year 25 is $55,340

Step-by-step explanation:

First we have to calculate the amount after 10 years (FV)

Annual payment (PMT): $1000

Tenor (Nper): 10 years

Rate: 9% compounded annually

Type 0 for payment at end of each year

In excel, we use formular FV(rate,Nper,-PMT,,type) = FV(9%,10,-1000,,0) = $15,193

Secondly, we continue put $15,193 for another 15 years with rate 9%

We can either use excel FV(rate,tenor,-PV) = FV(9%,15, -15193) = $55,340

or FV = PV * (1 + rate)^tenor = $15,193 * (1+9%)^15 = $55,340

Answer 2

The value in account at the end of year 25 is $55,340.

Step-by-step explanation:

Period for which payments are received = n = 10

Amount of each payment = P = $1,000

Compound interest rate = r = 9% = 0.09

Future value of annuity due

= (1 + r) x P x [((1 + r)^n) - 1] / r

= (1 + 0.09) x 1,000 x [((1 + 0.09)^10) - 1] / 0.09

= 1,090 x (1.3674 / 0.09)

= $16,560.29

Time for which this money is further invested = 25 - 11 = 14 years

This is because the money is first received at the end of year 10 (or the beginning of year 11).

Value in account at the end of year 25

= 16,560.29 x (1 + 0.09)^14

= $55,339.98

= $55,340 (rounded to the nearest dollar)