Question

​Recently, More Money 4U offered an annuity that pays 6.3 % compounded monthly. If $ 1,774 is deposited into this annuity every​ month, how much is in the account after 4 ​years? How much of this is​ interest?

Type the amount in the​ account:$

Type the amount of interest​ earned:$

Answer 1

Solution:

Calculation of Total amount available in the account after 4 years :

The formula for calculating the Future value of savings at the end of “t” years with “ n” compounding periods in a year is

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

Where FV = Future Value ; P = Periodic Deposit i.e.,

r = rate of interest   ; t = time in years   ; n = No. of compounding periods in a year

A per the information given in the question we have

P = $ 1,774    ; r = 6.3 % = 0.063 ; t = 4 years   ; n = 12 (since compounding is monthly )

To find FV = Future value

Applying the above values in the formula we have:

= $ 1,774 * [ [ ( 1 + ( 0.063 / 12 ) ) ( 4 * 12 )   - 1 ] / ( 0.063 / 12 ) ]

= $ 1,774 * [ [ ( 1 + 0.005250 ) 48   - 1 ] / 0.005250 ]

= $ 1,774 * [ [ ( 1.005250 ) 48   - 1 ] / 0.005250]

= $ 1,774 * [ [ 1.285748 - 1 ] / 0.005250 ]

= $ 1,774 * [ 0.285748 / 0.005250 ]

= $ 1,774 * 54.428229

= $ 96,555.677686

FV = $ 96,555.68 ( when rounded off to the nearest cent

Thus the amount available in the​ account after four years = $ 96,555.68

Calculation of Interest Earned :

The total amount of Interest can be calculated as follows

= Future value of the Investment in four years - ( Amount of each Monthly payment * No. of monthly Payments )

As per the information available we have

Amount of each Monthly payment = $ 1,774   ;   No. of monthly Payments = 48   ;

Future value of the Investment in four years = $ 96,555.68

Applying the above information in the formula we have

= $ 96,555.68 - ( $ 1,774 * 48 )

= $ 96,555.68 - $ 85,152

= $ 11,403.68

Thus the total amount of Interest earned = $ $ 11,403.68

Note: The value of ( 1.005250 ) 48   is calculated using the Excel formula =POWER(Number,Power)

=POWER(1.005250,48) = 1.285748