Question

Damian invests $6,000 today in an account earning 6% per year. How much is the investment worth in 5 years?

Group of answer choices

$8,029.35

$8,312.38

$6,000.00

$7,200.00

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 =Initial Investment ;   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

P = $ 6,000   ;   r = 6 % = 0.06 ; n = 1 ( Since compounding is annual ) ; t = 5 Years ; FV = $ To find    ;

Applying the above values in the formula we have

= $ 6,000 * ( 1 + ( 0.06 / 1 ) )^{1 * 5}

= $ 6,000 * ( 1 + 0.06 )⁵

= $ 6,000 * ( 1.06 ) ⁵

= $ 6,000 * 1.338226

= $ 8,029.353466

= $ 8,029.35 ( When rounded off to two decimal places )

Thus the future value of $ 6,000 invested now if the money is deposited for 5 years at an interest rate of 6 % is = $ 8,029.35

The solution is Option 1 : $ 8,029.35

Note : ( 1.06 ) ⁵ = 1.338226 is calculated using the excel function =POWER(Number,Power)

=POWER(1.06,5)