Question

Question 14 (3.3 points) Assume you are to receive a 10-year annuity with annual payments of $ 280. The first payment will be received today (that is, at t = 0) and the last payment will be received at the end of Year 9 (that is, at t = 9). You will invest each payment in an account that pays 13 percent. What will be the value in your account at the end of Year 20? (Round your answer to two decimal places and record without a dollar sign and without commas) Your Answer: Answer

Answer 1

We can use Future value (FV) of an Annuity due formula to find out the Future value of the annual deposit of $280 (as the payments are made at the starting of the year)

FV = PMT*(1+i) *{(1+i) ^n−1} / i

Where FV =?

PMT = Annual payment = $280

Annual interest rate = 13% per year

n = N = number of payments = 10

Therefore,

FV = $280 * (1+13%)* [(1+13%) ^10 -1]/13%

FV = $5,828.01 (this is the worth of annul deposits after 10 years but we have to calculate the worth of account at the end of year 20)

We can use following formula to calculate the future value (FV) or worth of the investment

FV = PV * (1+i) ^n

Where,

Present Value PV = $5,828.01 (future value in above calculation is present value in this calculation)

Future value of investment FV after 20 years =?

Annual interest rate i =13%

Time period n = 10 years

Therefore,

FV = $5,828.01 (* (1+ 13%) ^10

= $19,783.57

The Value of the account after the end of 20 years will be $19,783.57