Question

Find the savings plan balance after 2 years with an APR of 4% and monthly payments of $250. The balance is $ (Do not round until the final answer. Then round to the nearest cent as needed.) Enter your answer in the answer box O Type here to search

Answer 1

$6,506.51

Explanation:

Recall that increasing an amount C in x% is equivalent to multiply it by (1+x/100)

As we have 4% APR, the monthly interest would be (4/12)% = 0.04/12

Month 0 (first payment)

$250

Month 1

`250 + 250 (0.04)/(12)= 250((12.04)/(12))`

Month 2

`250(1+(12.04)/(12)+((12.04)/(12))^2)`

Month 3

`250(1+(12.04)/(12)+((12.04)/(12))^2+((12.04)/(12))^3)`

Month 24 (2 years)

`250(1+(12.04)/(12)+((12.04)/(12))^2+((12.04)/(12))^3+...+((12.04)/(12))^(24))`

The sum

`1+(12.04)/(12)+((12.04)/(12))^2+((12.04)/(12))^3+...+((12.04)/(12))^(24)`

is the sum of the first 24 terms of a geometric sequence with common ratio
`(12.04)/(12)` which is

`(1-(12.04/12)^(25))/(1-(12.04/12))=26.02603071`

so, after 2 years the saving balance is

250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.