Question

you decided to invest into a mutual fund that pays 3% per year, compounded monthly. how much should you invest now so that after 6 years from now, you will have $2,000 in the account? (round your answer to the nearest cent.)

Answer 1

To have $2,000 in the account after 6 years, you should invest approximately $1,672.45 now.

Step-by-step explanation:

To calculate the amount you should invest now, we can use the formula for compound interest, which is given by: A = P(1+r/n)^(nt) where A is the future value, P is the principal amount (the initial investment), r is the annual interest rate (in decimal form), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the principal amount is the amount you should invest now, the future value is $2,000, the annual interest rate is 3%, the interest is compounded monthly (so n = 12), and the number of years is 6.

Therefore, the formula becomes: 2,000 = P(1+0.03/12)^(12*6)

To solve for P, we can divide both sides of the equation by the term (1+0.03/12)^(12*6). This gives us: P = 2,000 / (1+0.03/12)^(12*6)

Using a calculator, we can find that P is approximately $1,672.45 (rounded to the nearest cent).