To find the future value of an account with compound interest, we use the formula:
A = P(1 + r/n)^(nt)
Where:
- A is the future value of the account, including interest
- P is the principal amount (the initial amount of money)
- r is the annual interest rate (decimal)
- n is the number of times that interest is compounded per unit t
- t is the time the money is invested for in years
Given:
- P = $38,000
- r = 3.19% per annum or 0.0319 as a decimal
- n = 12 (since the interest is compounded monthly)
- t = 15 years
Let's plug in these values into the formula:
A = 38000 * (1 + 0.0319/12) ^ (12 * 15)
First, divide the annual interest rate by the number of compounding periods per year:
0.0319 / 12 = 0.002658333
Next, add 1 to this value:
1 + 0.002658333 = 1.002658333
Then raise this to the power of the total number of compounding periods taking place over the course of the 15 years:
(1.002658333) ^ (12 * 15) = (1.002658333) ^ 180
Using a calculator to raise this to the power of 180, we get:
(1.002658333) ^ 180 ≈ 1.605459858
Now multiply this by the principal:
38000 * 1.605459858 ≈ 61007.47
After rounding to the nearest cent:
Future Value, A ≈ $61,007.47
Now, to separate this into thousands, dollars, and cents:
- Thousands = $61,007.47 // 1000 = $61
- Dollars = $61,007.47 % 1000 = $7 (but the full amount is $61,007, so it's actually $7,007)
- Cents = ($61,007.47 - $61,000 - $7) * 100 = $0.47 * 100 = 47 cents
Therefore, the future value of the account after 15 years is approximately:
- Thousands: 61
- Dollars: 7
- Cents: 47
