Question

5) Solve the problem.

A bank gives you two options to choose from for your investments:

Option A: 6% annual interest rate compounded yearly; and

Option B: 5.9% annual interest rate compounded quarterly.

Which of the two options is the better investment at the end of the 2 years.

6) Assuming the general level of inflation in Ghana is 15% per year; find the number of years it will take for prices to double. The currency of Ghana is called the cedi and its symbol is like that of the U.S. cent (¢), but placed in front of the quantitative amount like the dollar symbol.

7) A loan of $10,500 was given at an interest rate of 4% payable at the end of the fifth year. Find the continuous compound amount to be paid back.

Answer 1

Ans 5) Two year return will be given by following formula:

Return = (1 + interest rate/compounding period)^(n*compounding period) - 1

in case of option A.

return = (1 + .06/1)^(2*1) - 1

= 1.1236 - 1

= 12.36%

in case of option B

return = (1 + .059/4)^(2*4) - 1

= 1.124275 - 1

= 12.43%

Thus option B will give better return.

Ans 6) let the price of cedi will be double in n years

to find the value of n we will use following formula

2 = (1 + inflation rate)^n

2 = (1 + .15)^n

log (2) = n * log(1.15)

n = 4.96 years

thus the price will be double in 4.96 years (approx 5 years).

ans 7) Continuous compounded amount to be paid back can be given by following formula:

Amount = principal * e^(n*r)

where principal = $10500

r = 4%

n = 5 yrs

Amount = 10500 * e^(5*.04)

= $12824.73