Question

You want to purchase a new car in 8 years and expect the car to cost $16,000. 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 $16,000 in 8 years? 

You should invest $_______  each month.

Answer 1

Interest per month will be (0.065/12) = 0.0054167.

The total number of deposits will be 12×8 = 96.

Answer 2

SOLUTION :

Let $A be invested each month for 8 years to get $16000 at the end of the 8th year.

Usually deposits are made in the beginning of the month. In this case we assume the same. It is thus an annuity due case.

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 annuity due = A (1 + r)((1 + r)^n - 1) / (r)

=> 16000 = A * 1206.5/1200 ( (1206.5/1200)^96 - 1) / (6.5/1200)

=> 16000 = A * 126.157

=> A = 16000/126.157 

=> A = 126.83 ($)

So, $126.83 should be invested in the beginning of each month for 8 years to get $16000 at the end of 8th year. (ANSWER).

Note : 

if deposit is made at the end of each month, then,  A = 126.83 * (1206.5 / 1200) = 127.51 ($)