Question

11. Krishnan decide to begin saving towards the purchase of a new Toyota Highlander in 7 years. If he puts $4,000 at the beginning of each of the next 7 years in a savings account paying 7 percent compounded annually, how much will he accumulate after 7 years? Note: Krishnan is only making 7 payments, and the first payment is today. a. $33,575.35 b. $34,616.08 c. $35,750.74 d. $37,039,21 e. $41,969.19

Answer 1

In order to solve this problem, we shall be following the below steps:

We know, Future Value = Present Value ( 1 + r )ⁿ. So by using this formula, we shall compute the future value in different periods as shown below:

Future Value of $ 4,000 invested at the beginning of year 1:

= $ 4,000 ( 1 + 0.07 )⁷

= $ 6,423.13

Future Value of $ 4,000 invested at the beginning of year 2:

= $ 4,000 ( 1 + 0.07 )⁶

= $ 6,002.92

Future Value of $ 4,000 invested at the beginning of year 3:

= $ 4,000 ( 1 + 0.07 )⁵

= $ 5,610.21

Future Value of $ 4,000 invested at the beginning of year 4:

= $ 4,000 ( 1 + 0.07 )⁴

= $ 5,243.18

Future Value of $ 4,000 invested at the beginning of year 5:

= $ 4,000 ( 1 + 0.07 )³

= $ 4,900.17

Future Value of $ 4,000 invested at the beginning of year 6:

= $ 4,000 ( 1 + 0.07 )²

= $ 4,579.6

Future Value of $ 4,000 invested at the beginning of year 7:

= $ 4,000 ( 1 + 0.07 )¹

= $ 4,280

Now in order to compute the accumulated value, we shall add all the future values that we have computed above i.e.

= $ 6,423.13 + $ 6,002.92 + $ 5,610.21 + $ 5,243.18 + $ 4,900.17 + $ 4,579.6 + $ 4,280

= $ 37,039.21

So option d is the correct answer.

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