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

Since he joined the club on june 22nd,First deposit was made on 31 July second was on 31st August and last was 30 th September since termination date was October 18th there won't be any deduction for this month. Now lets calculate the time for which these deposits earned interest.

First deposit from july 31 to oct 18th = 79 days

Second deposit from 31st August to oct 18th= 48 days

Third 30 September = 18 days

Future value of $ 1 = (1+i)^(d/365)

Where

i = annual interest rate

d = no..of days the money was kept invested

Therefore total future of account =

150(1.03)^(79/365) +150(1.03)^(48/365) +150(1.03)^18/365 =451.77BD

Part b

Total contribution =150+150+150=450BD

Part c

Total interest earned = 451.77-450=1.77BD

Part e

Future value = present value (1+r)^p

Where

Present value =7000

Future value = 18000

r= semiannual interest rate = 5%/2= 2.5%

p= semiannual periods in total duration

Therefore

18000=7000(1.025)^p

Solving for p we get p= 38.248

These are semiannual periods which no. Of years would be =38.248/2= 19.124 years

I.e. it will take 19 years and 2 month for 7000 to become 18000 at the given rate