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

Accepted Solution

Answer:$6,506.51Step-by-step 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)% = 0.04/12Month 0 (first payment)$250Month 1[tex]250 + 250 \frac{0.04}{12}= 250(\frac{12.04}{12})[/tex]Month 2[tex]250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2)[/tex]Month 3[tex]250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3)[/tex]Month 24 (2 years)[tex]250(1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24})[/tex]The sum Β [tex]1+\frac{12.04}{12}+(\frac{12.04}{12})^2+(\frac{12.04}{12})^3+...+(\frac{12.04}{12})^{24}[/tex]is the sum of the first 24 terms of a geometric sequence with common ratio [tex]\frac{12.04}{12}[/tex] which is[tex]\frac{1-(12.04/12)^{25}}{1-(12.04/12)}=26.02603071[/tex]so, after 2 years the saving balance is250*26.02603071 = 6,506.50767= $6,506.51 rounded to the nearest cent.