Final answer:
To get $4,000 in 2 years with a savings bond paying 5% interest compounded monthly, you must invest approximately $3,710.80.
Step-by-step explanation:
To calculate the amount you must invest in a savings bond paying 5% interest that is compounded monthly to get $4,000 in 2 years, you can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (the initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
- Convert the interest rate to a decimal: 5% = 0.05.
- Plug in the given values into the compound interest formula:
A = P(1 + 0.05/12)^(12*2) - Simplify and solve for P:
4000 = P(1 + 0.0042)^(24)
P = 4000/(1 + 0.0042)^(24)
Using a calculator, you can find that P is approximately $3,710.80.