Question

4. (a) Suppose Fannie Rich wants to put her money in the bank so that she could get $5,000 in 5 years; if the bank is willing to pay annual interest of 2% for that amount of money, what is the value of Fannie’s money today?

(b) Using the Rule of 72 and the rate of 2%, Fannie could probably have doubled her money in how many years?

5. (a) What is the difference between simple and compound interests rates?

(b) What would have been the simple interest on Fannie’s $5,000 if she had just deposited the money for 5 years at the rate of 2%?

(c) Alternatively, what would have been the compound interest if interest was paid twice a year?

(d) Suppose interest had been compounded semi-annually, would the effective annually rate (EAR) had been different? Why? Why is the EAR important?

Please try to answer all questions. Thank you!

Answer 1

Question 4 (a)

Given the rate of Interest is 2% p.a.

Amount to be received after 5 years = $ 5,000.00

To find the Present Value of sum receivable, we multiply the Future Value by the annuity factor at year 5 @ 2%

To calculate the annuity factor we use the following formula:-

                =     1     ,                  =     1     ,              = 0.9057

                         (1+r)ⁿ                              (1.02)⁵

Hence the Value of Money today   = 0.9057 x 5,000.00 =4,528.50

Question 4 (b)

The Rule of 72 denotes the number of years taken to double the sum at any given rate. This rule is applied by dividing 72 by the given rate. In the Given Question, the Rate of Interest given is 2%.

Hence, the probable years when Fannie’s money would be double = 72 / 2 = 36 years.

Question 5 (a)

The Simple Interest Rate is calculated on the principal Loan amount for the whole period. In Simple Interest Rate the interest is not added to the Principal Amount for the purpose of calculating the Interest amount for the following period.

The Compound Interest is Basically Computed on Principal Amount and the Interest Amount thereon. In Compound Interest, the Interest Amount for the first period is added to the Principal Amount and the Interest for the Next year is calculated on Principal amount including the Interest Amount for the previous amount.

Question 5 (b)

Amount Invested by Fannie = $ 5,000.00

Simple Interest    = @2% p.a.

Interest for 1 year = $ 100.00

Interest for 5 years = $ 100.00 x 5   = $ 500.00

Total amount Receivable = $ 5,000.00 + $500.00   = $ 5,500.00

Question 5 (c)

Amount Invested by Fannie = $ 5,000.00

Compound Interest    = @2% payable twice a year.

Formula Future Value = P (1 + r/n)^nt

Where,

P    = Principal Amount

R    = Interest rate

N    = number of times interest applied per time period

T    = number of time period elapsed

Compound Interest Amount = 5,000 x (1 + 0.02/2)^{2 x 5} = $ 5,523.11

Question 5 (c)

EAR is used to compute the effective Interest Rate in case of Compound Interest Rates

EAR is calculated by the Formula = (1+i/n)ⁿ -1

EAR   = (1 + 0.02/10)¹⁰-1

          = 0.020180   = 2.02018 %

EAR is important as it denotes the annual Interest rate that is effective for the Interest calculations for the given amount for the given period.