Billy Burnett's grandfather willed Billy $10,000 payable on his twenty-first birthday. What will be the value of the bequest when Billy reaches 17 years of age if money is worth 8% compounded semi-annually?
I will not do all these either.
21 - 17 = 4 years = 8 periods at 4% per period
1.04^8 = 1.36856905
x * 1.36856905 = 10,000
x = $7306.90
To calculate the value of the bequest when Billy reaches 17 years of age, we can use the formula for compound interest. Here's how:
1. First, we need to determine the total number of compounding periods from the time of the bequest until Billy turns 21. Since the interest is compounded semi-annually, there are 2 compounding periods per year. Therefore, the number of compounding periods is (21 - 17) * 2 = 8.
2. Next, we can calculate the interest rate per period. Given that the money is worth 8% compounded semi-annually, we divide the annual interest rate by the number of compounding periods per year: 8% / 2 = 4% = 0.04 as a decimal.
3. Now we can use the compound interest formula to find the future value of the bequest:
Future Value = P * (1 + r/n)^(n*t)
P = Principal amount (initial bequest) = $10,000
r = Annual interest rate = 8% = 0.08 as a decimal
n = Number of compounding periods per year = 2
t = Number of years until Billy turns 21 = (21 - 17) = 4
Plugging these values into the formula, we have:
Future Value = $10,000 * (1 + 0.08/2)^(2*4)
4. Calculating this expression, we get:
Future Value = $10,000 * (1.04)^8
Future Value ≈ $10,000 * 1.36048703
Therefore, the value of the bequest when Billy reaches 17 years of age will be approximately $13,604.87.