Question

8. Ann deposited RM1,000 in a bank account, and 10 years later she closes out the account,
which is worth RM2,158.90. What annual rate of interest has she earned over the 10
years?

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 = Number of compounding periods per year ;    t = Time in years    ;

As per the information given in the question we have

FV = RM 2,158.90   ; P = RM 1,000    ; n = 1   ;   t = 10 ; r = To find ;

Applying the above values in the formula we have

2,158.90 = 1,000 * ( 1 + ( r / 1 ) ) ( 1 * 10 )

2,158.90 = 1,000 * ( 1 + r )10

2,158.90 / 1,000 = ( 1 + r ) 10

2.15890 = ( 1 + r ) 10

( 1 + r ) 10 = 2.15890

1 + r = ( 2.15890 ) 1 / 10

1 + r = ( 2.15890 ) 0.10

1 + r = 1.079999

r = 1.079999 – 1

r = 0.079999

r = 7.9999 %

Thus the annual rate of return earned by Ann over the 10 years is  

r = 7.99 % ( when rounded off to two decimal places )

r = 8.00 % ( when rounded off to the nearest dollar )

Note: ( 2.158900 ) ( 0.10) = 1.079999 is calculated using the excel formula =POWER(Number,Power)

=POWER(2.15890,0.10)