How much money should be invested at an annual interest rate of 6.2% compounded continuously, to be worth at least $58,000 after 13 years.
x e^(.062(13)) ≥ 58000
x ≥ 58000/e^(.062(13))
x ≥ 25905.18
719.60 $
To calculate the amount of money that should be invested at an annual interest rate of 6.2% compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the future value of the investment
P = the principal amount (the initial investment)
e = the base of the natural logarithm (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time in years
In this case, we want to find the principal amount (P) that will result in a future value (A) of at least $58,000 after 13 years. So, we can rearrange the formula to solve for P:
P = A / e^(rt)
Substituting the given values into the formula:
P = 58000 / e^(0.062 * 13)
Calculating this expression:
P ≈ 58000 / 3.6896051
P ≈ 15723.195
Therefore, approximately $15,723.20 should be invested to be worth at least $58,000 after 13 years at an annual interest rate of 6.2% compounded continuously.