Question

You want to purchase a new car in 3 years and expect the car to cost $30,000. Your bank offers a savings 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 $30,000 in 3 years?

Answer 1

SOLUTION :

Let $A be invested each month for 3 years to get $30000 at the end of the 3rd year.

We assume, deposits are made at 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 = 3 * 12 = 36 months.

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

=> 30000 = A * ((1205.5/1200)^36 - 1) / (5.5/1200)

=> 30000 = A * 39.04333145

=> A = 30000/39.04333145

=> A = 768.38 ($)

So, $768.38 should be invested in the end of each month for 3 years to get $ 30000 at the end of 3rd year. (ANSWER).