Question

1. Time Value of Money  
   1. What is the present value of a $2,000 lump sum to be paid in six years if interest rate is 5%?                                                                      
   2. Suppose you deposit $1,000 today in an account that pays 8% APR. How many yearswill it take the account balance to grow to $3,000 if interest is compounded quarterly?

Answer 1

a. The amount is computed as shown below:

Present value = Future value / (1 + r)ⁿ

So, the amount will be computed as follows:

= $ 2,000 / 1.05⁶

= $ 1,492.43 Approximately

b. The number of years is computed as shown below:

Future value = Present value (1 + r)ⁿ

$ 3,000 = $ 1,000 (1 + 0.08 / 4) ^{n x 4}

3 = 1.02 ⁴ⁿ

Taking log both sides, we shall get:

log 3 = 4n log 1.02

1.098612289 = 4n x 0.019802627

1.098612289 / 0.019802627 = 4n

55.47810766 / 4 = n

13.87 years Approximately = n

Feel free to ask in case of any query relating to this question