Question

You want to purchase a new car in 8 years and expect the car to cost $83,000. Your bank offers a plan with a guaranteed APR of 6.5% if you make regular monthly deposits. How much should you deposit each month to end up with $83,000 in 8 years?

Answer 1

SOLUTION :

Let $A be invested each month for 8 years to get $83000 at the end of the 8th year.

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

Interest rate per month, r = 6.5/12 % = 6.5/1200 

=> (1 + r) = 1 + 6.5/1200 = 1206.5/1200 

Number of periods, n = 8 * 12 = 96 months.

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

=> 83000 = A * ((1206.5/1200)^96 - 1) / (6.5/1200)

=> 83000 = A * 125.4773481

=> A = 83000/125.4773481

=> A = 661.47 ($)

So, $661.47 should be invested in the end of each month for 8 years to get $ 83000 at the end of 8th year. (ANSWER).