Question

Two years ago, you invested $2,650. Today, it is worth $3,450. What rate of interest did you earn?

a) 4.31 percent

b)14.10 percent

c)7.05 percent

d)1.18 percent

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 of Investment       ; P = Principal   ;   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 = $ 3,450 ; P = $ 2,650   ; n = 1   ;   t = 2 ; r = To find ;

Applying the above values in the formula we have

3450 = 2650 * ( 1 + ( r / 1 ) ) ^{( 1 * 2 )}

3450 = 2650 * ( 1 + r ) ²                                   

3450 / 2650 = ( 1 + r ) ²

1.301887 = ( 1 + r ) ²

( 1.301887 ) ^½ = ( 1 + r )

( 1 + r ) = ( 1.301887 ) ^½

1 + r = 1.141003

r = 1.141003 – 1

r = 0.141003

r = 14.1003 %

r = 14.10 % ( when rounded off to two decimal places )

Thus the rate of interest earned = 14.10 %

The solution is Option b) 14.10 percent

Note : ( 1.301887 ) ² = 1.141003 is calculated using the excel formula =POWER(Number,Power)

=POWER(1.301887,2)