Question

if you deposit 10,697 dollars into a savings account, what interest would you need to be earning to have 19,962 dollars in the same account 4 years later? answer as a percent to the nearest hundredth of a percent as in xx.xx %

Answer 1

Solution:

The formula for calculating the future value of an Investment with compound Interest is

FV = P * ( 1 + (r/n) ) ^{n * t}

Where

FV = Future value   ; P = Principal amount or initial amount invested ;   r = rate of interest   ;

n = No. of compounding periods per year ; t = Time in years

As per the information given in the question we have

FV = $ 19,962   ; P = $ 10,697    ; n = 1   ;   t = 4 ;   r = To find    ;

Applying the above values in the formula we have

19,962 = 10,697 * ( 1 + ( r / 1 ) ) ^{( 1 * 4 )}

19,962 = 10,697 * ( 1 + r ) ⁴

19,962 / 10,697 = ( 1 + r ) ⁴

1.866131 = ( 1 + r ) ⁴

( 1 + r ) ⁴ = 1.866131

1 + r = ( 1.866131 ) ^{1 / 4}

1 + r = ( 1.866131 ) ^0.25

1 + r = 1.168787

r = 1.168787 – 1

r = 0.168787

r = 16.8787 %

r = 16.88 % ( when rounded off to two decimal places )

Thus the annual rate of interest that will have to be earned = 16.88 %

Note: ( 1.866131 ) ^{( 0.25 )} = 1.168787 is calculated using the excel function =POWER(Number,Power)

=POWER(1.866131,0.25)