Question

12. Non annual compounding period

The number of compounding periods in one year is called compounding frequency. The compounding frequency affects both the present and future values of cash flows.

An investor can invest money with a particular bank and earn a stated interest rate of 13.20%; however, interest will be compounded quarterly. What are the nominal (or stated), periodic, and effective interest rates for this investment opportunity?

Interest Rates
Nominal rate
Periodic rate
Effective annual rate

Hubert needs a loan and is speaking to several lending agencies about their interest rates and loan terms. He particularly likes his local bank because he is being offered a nominal rate of 12.00%. However, since the bank is compounding its interest daily, the loan will impose an effective interest rate of   on his loan.

Suppose you decide to deposit $14,000 into a savings account that pays a nominal rate of 15.60%, but interest is compounded daily. Based on a 365-day year, how much would you have in your account after six months? (Hint: To calculate the number of days, divide the number of months by 12 and multiply by 365.)

$14,680.34

$14,831.68

$15,134.37

$15,437.06

Answer 1

Answer a.

Nominal Rate = 13.20%

Periodic Rate = Nominal Rate / Compounding Per Annum
Periodic Rate = 13.20% / 4
Periodic Rate = 3.30%

Effective Annual Rate = (1 + Periodic Rate)^Compounding Per Annum - 1
Effective Annual Rate = (1 + 0.0330)^4 - 1
Effective Annual Rate = 1.1387 - 1
Effective Annual Rate = 0.1387 or 13.87%

Answer b.

Annual Interest Rate = 12.00%

Daily Interest Rate = 12.00% / 365
Daily Interest Rate = 0.032877%

Effective Interest Rate = (1 + Daily Interest Rate)^365 - 1
Effective Interest Rate = (1 + 0.00032877)^365 - 1
Effective Interest Rate = 1.1275 - 1
Effective Interest Rate = 0.1275 or 12.75%

Answer c.

Annual Interest Rate = 15.60%

Daily Interest Rate = 15.60% / 365
Daily Interest Rate = 0.042740%

Time Period = 365 days * 6 / 12
Time Period = 182.50 days

Future Value = Amount Deposited * (1 + Daily Interest Rate)^Time Period
Future Value = $14,000 * 1.00042740^182.50
Future Value = $14,000 * 1.0811052
Future Value = $15,134.37