Find the Principal Value of an Investment

Question

  An investment sum up to $10,000 in 6 months, which pays 5% compounded semi-annually. What is the principal value?

Answer 1

$9756

10,000 = P(1+r/n)^nt = P(1+.05/2)^2(1/2) = P(1+.025)^1 = P(1.025)

where P = original amount, n=number of compounding periods per year, t = time measured in years

P = 10,000/1.025 = $9756.097561 =$9756.10 = $9756 rounded to nearest dollar

= $9756.10 rounded to nearest cent

Answer 2

Assume the 5% is an annual percentage rate (APR). So the semi-annual rate is 0.05/2 = 0.025 every 6 mos.

You're asking for the principal if the account is worth $10,000 after six months. That's only one semi-annual compounding period. So the expression is 10,000 = P(1 + 0.05/2)¹. You should be able to solve that for P. Remember to use order of operations rules.