Question

Amy is going to need R145 000 in three years’ time, to pay for a holiday overseas. She immediately starts
to make monthly deposits into an account earning 11,05% interest per year, compounded monthly. Amy’s
monthly deposit is
[1] R3 384,18.
[2] R3 415,34.
[3] R4 027,78.
[4] R4 707,20.
[5] R4 750,55.

Answer 1

Solution:

The formula for calculating the Future value of savings at the end of ” n “ months with monthly compounding is

FV = P * [ [ ( 1 + r ) ⁿ- 1 ] / r ]

Where FV = Future value of savings   ; P = Periodic Deposit i.e., Fixed amount of Monthly deposit

r = monthly rate of interest   ; n = no. of months

A per the information given in the question we have

FV = R 145,000

Annual Interest rate = 11.05 % = 0.1105

Thus Monthly interest rate = 0.1105 / 12 =   0.0092083               ( Since the compounding is monthly )

Thus r = 0.0092083

The monthly deposits are to be made for a period of 3 years

Converting the same into months we have

= 3 * 12 months = 36 months

Thus n = 36

To find P = Monthly deposit

Applying the above values in the formula we have:

145,000 = P * [ [ ( 1 + 0.0092083 ) ³⁶   - 1 ] / 0.0092083 ]    

145,000 = P * [ [ ( 1.0092083 ) ³⁶   - 1 ] / 0.0092083 ]

145,000 = P * [ [ 1.3909429 - 1 ] / 0.0092083 ]

145,000 = P * [ 0.3909429 / 0.0092083 ]

145,000 = P * 42.4554912

Thus P = 145,000 / 42.4554912

P = 3,415.3415

P = 3,415.34 (When rounded off to two decimal places )

Thus the Solution is Option 2. R 3,415.34

Thus if Amy starts to make monthly deposits into an account earning 11.05% interest per year, compounded monthly, Amy’s monthly deposit should be is R 3,415.34 to receive R 145,000 at the end of three years.

Note: The value of ( 1.0092083 ) ³⁶   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.0092083,36) = 1.3909429