You find a mutual fund that offers approximately 5% APR compounded monthly. You will invest enough each month so that you will have $1000 at the end of the year. How much money will you have invested in total after one year?

Accepted Solution

Answer:The amount you need to invest in a year is $951.3Step-by-step explanation:Consider the provided information.The future value can be calculated as:[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where, A represents future value, P represents Principal value, r represents interest rate in decimal, n represents number of time interest is compounded and t represents time in years.Now use the above formula to find the money needed to invest i.e P.Substitute, n = 12 , t = 1, A = 1000 and r = 5% or 0.05 in the above formula.[tex]1000=P(1+\frac{0.05}{12})^{12 \times 1}[/tex][tex]1000=P(1.00417)^{12}[/tex][tex]1000=P(1.0512)[/tex][tex]P=951.3[/tex]Thus, the amount you need to invest in a year is $951.3