Question

mework: Week 5 Homework e: 0 of 1 pt 20 of 38 (12 complete) HW Score: 28.95%, 11 of 38 pts 25 Question Help want to purchase a new car in 4 years and expect the car to cost S83.000. Your bank offers a plan with a guaranteed APR of 55% if you make regular monthly deposits How ch should you deposit each month to end up with $83,000 in 4 years? u should invest s each month. ound the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed ) Enter your answer in the answer box and then click Check Answer All parts showing OType hene to ALIENWARE no

Answer 1

》の g 3000x 4x5.5 182. 0 18260-380 .416663. month 후 wよ 4 8 380.42

Answer 2

SOLUTION :

Let $A be invested each month for 4 years to get $83000 at the end of the 4th year.

We assume the 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 = 4 * 12 = 48 months.

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

=> 83000 = A * ((1205.5/1200)^48 - 1) / (5.5/1200)

=> 83000 = A * 53.5528518

=> A = 83000/53.5528518

=> A = 1549.87 ($)

So, $1549.87 should be invested in the end of each month for 4 years to get $ 83000 at the end of 4th year. (ANSWER).