Question

1.   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

1

a.

Given future value FV= $2000

Paid lumpsum

Time t= 6 years

Interest rate r = 5%

Present value = FV/ (1+r)^t

= 2000 / (1+ 0.05)^6 = 1492.430793

Therefore Present Value = $1492.43

b.

deposit P = 1000

interest rate = 8% per annum

compounded quarterly = interest rate r = 8% /4 = 2%

let time = t years

A = P (1+r/n)^nt

Here quarterly implies n =4

3000 = 1000 * (1+ 0.08/4)^4t

3 = 1.02^4t

Taking logarithm on both sides

log(3) = log (1.02^4t)

4t * log (1.02) = log(3)

4t = log(3)/ log (1.02)

4t = 55.478

t = 55.478/4 = 13.8695

Therefore it will take approximate of 14 years for the balance to grow to $3000.