Mona Persian is considering a new investment fund with a semiannual interest rate of 2.5%. Any money she invests would have to be left in it for at least five years if she wanted to withdraw it without a penalty. a) What is the nominal interest rate? b) What is the effective annual interest rate? c) If Mona deposits $10,000 in the fund now, how much should it be worth in five years?

Explanation:

a.)

2.5% rate in the question is the semi-annual rate i.e. six-month interest rate. This means that there are two interest payments per year. To find the annual nominal rate, multiply the semi-annual rate by 2 since there are two semi-annual periods per year. Nominal rate is also referred to as the Annual Payable Rate(APR). Therefore,

Nominal rate = 2.5% *2

Nominal rate = 5%

b.)

Effective interest rate is the EAR.  You use the Annual Percentage Rate (APR) to calculate EAR.

The formula is as follows;

EAR =

where m = number of compounding periods per year

Next, plug in the numbers to the above formula and solve;

EAR =

EAR = 1.0506 -1

EAR = 0.0506 OR 5.06%

c.)

If Mona deposits $10,000 in the fund now, use the nominal rate to calculate its future value in five years.

FV = PV(1+r)^n

r = semi-annual rate = 2.5%

PV = principal deposited = 10,000

n = total duration of investment = 2 * 5 = 10

FV = 10,000(1+0.025)^10

FV = 10,000*1.28008

FV = $12,800.85

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