Question

Assume the inflation rate is 356% APR, compounded annually. Would you rather eam a nominal return of 4.72% APR, compounded semiannually, or a teal rebum of 296% APR compounded quarterly? (Note: Be careful not to round ary intermediate sleps less than six decimal places) To put these on the same basis, you mast convert them both to nominal EARs The EAR for 472% APR, compounded semiannually in (Type your anower in decimal format Round to six decimal places)

Answer 1

To compare the options, we convert their interest rates to equivalent annual effective interest rates (EAR). The nominal return of 4.72% APR compounded semiannually has an EAR of 0.095057, while the real return of 296% APR compounded quarterly has an EAR of 1.98256. The real return option is better.

To compare the two options - nominal return of 4.72% APR compounded semiannually and a real return of 296% APR compounded quarterly - we need to calculate their equivalent annual effective interest rates (EAR).

For the nominal return of 4.72% APR compounded semiannually:

1. Convert the annual nominal interest rate to a semiannual nominal interest rate: 4.72% APR divided by 2 = 2.36% per six months.
2. Convert the semiannual nominal rate to an effective interest rate: (1 + 0.0236)^2 - 1 = 0.047248 - 1 = 0.047248.
3. Convert the effective interest rate to an EAR: (1 + 0.047248)^2 - 1 = 0.095057 - 1 = 0.095057.

The EAR for a nominal return of 4.72% APR compounded semiannually is 0.095057 (rounded to six decimal places).

For the real return of 296% APR compounded quarterly:

1. Convert the annual real interest rate to a quarterly real interest rate: 296% APR divided by 4 = 74% per quarter.
2. Convert the quarterly real rate to an effective interest rate: (1 + 0.74)^4 - 1 = 1.9926 - 1 = 0.9926.
3. Convert the effective interest rate to an EAR: (1 + 0.9926)^2 - 1 = 2.98256 - 1 = 1.98256.

The EAR for a real return of 296% APR compounded quarterly is 1.98256 (rounded to six decimal places).

Comparing the two EARs, the nominal return of 4.72% APR compounded semiannually has an EAR of 0.095057, while the real return of 296% APR compounded quarterly has an EAR of 1.98256. Therefore, the real return of 296% APR compounded quarterly is a better option.