Question

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.

Find the present value of $10,000 if interest is paid at a rate of 5% per year, compounded weekly, for 2 years. (Round your answer up to the nearest cent.)

Answer 1

solution

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 . . .

compounded weekly so n =52

10,000 = P(1 + .05/52)^{52 * 2}

10,000 = P(1.00096)¹⁰⁴

10,000/(1.00096)¹⁰⁴ = P . . . use the exact value to avoid rounding errors!

9050.25546 = P

present value = $ 9050.26