The present value of a sum of money is the amount that must be invested now, at a given rate of interest, to produce the desired sum at a later date.

Question

Find the present value of $10,000 if interest is paid at a rate of 5% per year, compounded quarterly, for 2 years (round to the nearest cent) 

Answer 1

Hi Sara,

 

You'll need the compound interest formula

 

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

 

A is the amount you end up with

P is the "present value" (usually called the "principal")

r is the interest rate as a decimal

n is the number of compoundings a year

t is the number of years

 

So substitute the values you're given . . .

 

10,000 = P(1 + .05/4)^{4 * 2}

10,000 = P(1.0125)⁸

10,000/(1.0125)⁸ = P    . . . use the exact value to avoid rounding errors!

 

9,053.98 = P