You currently have $5000 in a savings account that pays 6% interest per year. Interest is compounded monthly. You add another $200 each month. What do you have on your savings account after five years, and what is the total interest earned during these five years?
Accepted Solution
A:
Answer:At the end of the five years you will have $20698.26 in your bank account from which $3698.26 correspond to the interest earned during the five years. Step-by-step explanation:We need to take into account the following formulasCompound interest for a principal is:[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Future value of a serie is:[tex]A= PMT(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}})[/tex]To know the savings after five years we have to add the compund interest for principal with the future value of a serie. [tex]A=P(1+\frac{r}{n})^{nt} +PMT(\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}) [/tex]Where:A = future value wih of the loan with interestP = Principal InvestmentPMT = Monthly paymentr =annual interest rate (decimal)n = The number of times that interest is compounded per unit of timet = Time the money is investedSo we have that P = $5000 PMT = $200 r = [tex]\frac{6}{100} = 0.06 (decimal)[/tex] n= 12 t = 5Replace the values[tex]A=5000(1+\frac{0.06}{12})^{12*5} +200(\frac{(1+\frac{0.06}{12})^{12*5}-1}{\frac{0.06}{12}}) [/tex]Solve it[tex]A=5000(1+0.005)^{60} +200(\frac{(1+0.005)^{60}-1}{0.005}) [/tex][tex]A=5000(1.005)^{60} +200(\frac{(1.005)^{60}-1}{0.005}) [/tex][tex]A=5000(1.34885) +200(\frac{1,34885-1}{0.005}) [/tex][tex]A=6744,25 +200(\frac{0,34885}{0.005}) [/tex][tex]A=6744,25 +200(69.77) [/tex][tex]A=6744,25 +13954.01 [/tex][tex]A=20698.26 [/tex]At the end of the five years you will have $20698.26 in your bank accountTo know the total interest earned during the five year we have to substract the total (A) with the initial investment (P) and the aditions during the five years (MA)I = A - (P+MA)A = $20698.26 P = 5000 MA = (12x5x200) = $12000Replace I = 20698.26 - (5000 + 12000)I = 20698.26 - (17000)I = 3698.26The total interest earned during the five years were $3698.26