Question

You want to purchase a new car in 6 years and expect the car to cost $88,000. Your bank offers a plan with a guaranteed APR of 5.5% If you make regular monthly deposits. How much should you deposit each month to end up with $88,000 in 6 years? You should invest $ each month. (Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed.)

Answer 1

Here, we have Future Value = $88,000

Monthly interest rate (r) = 0.45833333% per month [5.50% / 12 Months]

Number of periods (n) = 72 Years [6 Years x 12 months]

Monthly payments (P) = ?

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)n - 1} / r ]

$88,000 = P x [{(1 + 0.0045833333)72 - 1} / 0.0045833333]

$88,000 = P x [(1.389919807 – 1) / 0.0045833333]

$88,000 = P x [0.389919807 / 0.0045833333]

$88,000 = P x 85.07341249

P = $88,000 / 85.07341249

P = $1,034.40 per month

“Hence, we should invest $1,034.40 each month”

Answer 2

SOLUTION :

Let $A be invested each month for 6 years to get $88000 at the end of the 6th year.

We assume, deposits are made in the end of each month. 

Interest rate per month, r = 5.5/12 % = 5.5/1200 

=> (1 + r) = 1 + 5.5/1200 = 1205.5/1200 

Number of periods, n = 6 * 12 = 72 months.

So, FV of above annuity = A ((1 + r)^n - 1) / (r)

=> 88000 = A * ( (1205.5/1200)^72 - 1) / (5.5/1200)

=> 88000 = A * 85.0734

=> A = 88000/85.0734

=> A = 1034.40 ($)

So, $1034.40 should be invested in the end of each month for 6 years to get $ 88000 at the end of 6th year. (ANSWER)