Question

A sum of $120,000 now at an interest rate of 10% per year compounded semiannually is equivalent to how much money 6 years ago? Solve using the effective annual ate and the effective semiannual rate.

Answer 1

So, basically you are asking what was the value of $120,000 (10% comp semi-annual) six yeas ago?
Comp interest formula is:
Total = Principal × ( 1 + Rate )^years we can rephrase that as:
Principal = Total ÷ (1 + Rate)^years
10% compounded annually =
10.25% semi-annually
Principal = 120,000 ÷ (1+ .01025)^6
Principal = 120,000 ÷ 1.0630976416
Principal = 112,877.68 six years ago

To check that, let's see that amount compounded for 6 years.
Total = Principal × ( 1 + Rate )^years
Total = 112,877.68 x (1.01025)^6
Total = 120,000