Question

Time Value of Money

a. What is the present value of a $2,000 lump sum to be paid in six years if interest rate is 5%?

b. Suppose you deposit $1,000 today in an account that pays 8% APR. How many years will it take the account balance to grow to $3,000 if interest is compounded quarterly?

Answer 1

Answer to (a)

Given , Future Value after 6 years = $2000 (FV)

Interest rate = 5% (i)

Present Value = ? (PV)

n = 6 years

Formula # Future Value = Present value * (1+i)^n #

$2000 = PV* (1.05)^6

By solving the above equation we get Present value as $1492.43 approximated to 2 decimal values.

Assumptions : As there is no information regarding the compounding period, it is assumed that compounding is done annually.

Answer to (b)

Given, Present value = $1000 (PV)

Future value = $3000 (FV)

Interest rate per annum = 8% (i)

We should find the period it takes for the PV to become FV at the given i considering the fact that compounding has done Quarterly.

Formula # FV = PV * (1+i/4)^4n #  

$3000 = $1000 * (1.02)^4n

By solving the above equation we get n= 13.86 years approximated to two decimals

Note - How to Solve above equation?

$3000 = $1000 * (1.02)^4n

$3 = (1.02)^4n

Apply Log on both sides

Log 3 = 4n Log (1.02)

0.47712 = 4n Log (102/100)

0.47712 = 4n[ Log (102) - Log (100)]

we get n = 13.86