Question

A savings plan requires 48 deposits of $500 per month commencing today. If the interest rate is 14.9% p.a compounding monthly, the value of the investment plan in exactly 4 years from today will be closest to: Select one: a. $32948.94 b. $32544.84 c. $2864.52 d. $2493.06

Answer 1

Solution:

The formula for calculating the Future value of savings at the end of “ n” months with monthly compounding , where the first payment is made at the beginning of the first period

FV = P * [ ( ( 1 + r ) n   – 1 ) / r ] * ( 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

P = $ 500   ;

Annual Interest rate = 14.90 % = 0.1490

Thus Monthly interest rate = 0.1490 / 12 =   0.012417                ( Since the compounding is monthly )

Thus r = 0.012417

The monthly deposits are to be made for a period of 4 years

Converting the same into months we have

= 4 * 12 months = 48 months

Thus n = 48

To find FV = Future value of Investment

Applying the above information in the formula we have

= $ 500 * [ ( ( 1 + 0.012417 )( 48 ) – 1 ) / 0.012417 ] * ( 1 + 0.012417 )

= $ 500 * [ ( ( 1.012417 )48 – 1 ) / 0.012417 ] * 1.012417

= $ 500 * [ ( 1.808197 – 1 ) / 0.012417 ] * 1.012417

= $ 500 * [ 0.808197 / 0.012417 ] * 1.012417       

= $ 500 * 65.089686 * 1.012417

= $ 32,948.941473

= $ 32,948.94 ( when rounded off to two decimal places )

Thus the value of the investment plan in exactly 4 years from today will be closest to Option a. $ 32,948.94

Note: The value of ( 1.012417 ) 48   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.012417,48) = 1.808197