Question

Five years from today, you plan to invest $2,950 for 8 additional years at 5.3 percent compounded annually. How much will you have in your account 13 years from today?

Multiple Choice $4,962.80 $4,459.12 $4,845.57 $3,819.12

Answer 1

Solution:           

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

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

Where

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

P = $ 2,950   ; r = 5.3 % = 0.053 ; n = 1   ;   t = 8  

Applying the above values in the formula we have

= $ 2,950 * ( 1 + ( 0.053 / 1) ) ^{( 8 *1 )}

= $ 2,950 ( 1 + 0.053 ) ⁸                                    

= $ 2,950 * ( 1.053 ) ⁸

= $ 2,950 * 1.511565

= $ 4,459.1168

= $ 4,459.12 ( when rounded off to two decimal places )

Thus the amount that will be available in the account 13 years from today is = $ 4,459.12

The solution is Option 2 = $ 4,459.12

Note : ( 1.053 ) ⁸ = 1.511565 is calculated using the excel formula =POWER(Number,Power)

=POWER( 1.053, 8)