Question

On June 22, Ali joined a gulf club. His bank will automatically deduct BD 150 from his checking
account at the end of each month, and deposit it into his gulf club account, where it will earn
3% annual interest. The account comes to term on October 18. Find the following:
a. Find the future value of Ali’s gulf club account. ( 3 Marks )
b. Find Ali’s total contribution to the account. (1 Mark)
c. Find the total interest earned on the account. (1 Mark)
3. How long will it take BD 7000 to accumulate to BD 18,000 if the interest is at 5% compounded
semi- annually?

Answer 1

Number of days compounding happens = Oct 18 - Jun 22 = 118 days

From June till September, BD 150 will be deducted each month and deposited in the gulf club account.

(1+r)^365 = (1+3%)

r = (1+3%)^(1/365)-1 = 0.0081% (effective daily interest rate)

Date of deposit every month	Number of days (n) (18 Oct - Date of deposit)	Amount/month	FV of amount (Amount*(1+r)^n)
22-Jun	118	150	151.4402701
22-Jul	88	150	151.072794
22-Aug	57	150	150.6940054
22-Sep	26	150	150.3161665
18-Oct
		Total	603.5232359

a). FV of Ali's gulf club account = BD 603.52

b). Ali's total contribution to the account is the total deposits made = 4*150 = BD 600

c). Total interest earned = FV of the account - deposits made = 603.52 - 600 = BD 3.52

3). PV = -7,000; FV = 18,000; I = 2.5%, solve for nper.  

Number of compoundings = 38.2486

So, number of years it will take for BD 7,000 to accumulate to BD 18,000 is 38.2486/2 = 19.12 years

Note: If the semi-annual compounding rate is 5% (it is not clearly stated in the question if the 5% is the annual or semi-annual rate), then number of years will be 9.68 years.