Question

Upon graduation from college in two years you plan to go for an extravagant European vacation. Your parents will give you a graduation gift of $3,600 to help with the cost of the vacation. You have $2,000 available at present, which you plan to deposit into an account that pays 11.5 percent interest compounded quarterly. What is the maximum amount you will be able to spend on your vacation?

Answer 1

Solution :

The maximum amount that can be spend on vacation = Amount given by parents on graduation after two years + Principal invested and interest earned on investment of $ 2,000 deposited into an account that pays 11.5 percent interest compounded quarterly

As per the information given in the question we have

Amount given by parents on graduation after two years = $ 3,600

Calculation of Principal invested and interest earned on investment of $ 2,000 into an account that pays 11.5 percent interest compounded quarterly

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 Investment today   ;   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 = $ 2,000   ;   r = 11.5 % = 0.115 ; n = 4 ( Since compounding is quarterly ) ;  

t = 2 Years ; FV = $ To find    ;

Applying the above values in the formula we have

= $ 2,000 * [ ( 1 + ( 0.115 / 4 ) )^{4 * 2} ]

= $ 2,000 * [ ( 1 + ( 0.115 / 4 ) )⁸ ]

= $ 2,000 * [ ( 1 + 0.028750 )⁸ ]

= $ 2,000 * ( 1.028750 )⁸

= $ 2,000 * 1.254523

= $ 2,509.046912                      

= $ 2,509 ( When rounded off to the nearest dollar )

Note : ( 1.028750 ) ⁸ = 1.254523 is calculated using the excel formula =POWER(Number,Power) =POWER(1.028750,8)

Thus the maximum amount that can be spend on vacation = $ 3,600 + $ 2,509

= $ 6,109

The solution is = $ 6,109