Question

Ms. Alicia Weir has been able to accumulate $10,000 in savings from her end-of-month salary and is seeking to invest this amount plus the regular monthly salary savings of $400 into a suitable investment. Given her risk profile, the People’s Preference Credit Union has been selected as the best financial intermediary to place her funds. The credit union has offered her a high-interest savings account with an interest rate of 8% compounded monthly for the next 4 years for the investment of Alicia’s accumulated and ongoing savings.

            a) What effective interest rate will Alicia be earning on her funds?

b)    What is the expected balance of the high-interest savings account at the end of the 4-year term?

Answer 1

a)

Given interest rate = 8%

Interest is compounded monthly

Time period 4 years

Effective annual interest rate = (1 + nominal interest rate / n)ⁿ – 1

n= number of times compounded per year

= (1 + 0.08/12)¹² – 1 = 0.0829 = 8.29%

b)

Amount invested = accumulated amount + ongoing savings = $10,000 + $400

Amount invested is compounded monthly for 4 years, so after 4 years, the balance amount i.e., the total amount is calculated by using below formula

Amount = Principal * ( 1+ interest rate/ n)^n*t

n= number of times compounded per year

t= time period

amount = 10400 * (1+ 0.08/12)^12*4

= 10400 * 1.37566 = $14,306.864

Balance amount after 4 years = $14,306.86