Interest Formula

Question

Find the present value of $10,000 if interest is paid at a rate of 6% per year, compounded weekly, for 4 years. (Round your answer to the nearest cent.)

Answer 1

I will assume that $10,000 is the total amount (principle and interest) at the end of year 4. (Otherwise, present value is $10,000 :-) )

Let's call present value x. Per week interest is 6/52 %, 4 years is 4*52 weeks

After 4 years, with compounded interest weekly, we will have

x * (1+6/52/100)^(4*52)=x * (1+0.001154)²⁰⁸ = x*1.271 = 10000

x = 10000/1.271 = $7867.82