Jose invests $4000 in an investment account paying 8% annually for 12 years. Suppose the interest was compounded quarterly instead of annually.
How much would the future value of the investment increase?
Enter your answer as a dollar amount, such as: $302.26
P1 = Po(1+r)^n. Compounded annually.
r = annual % rate.
n = the number of compounding periods.
P1 = 4000(1+0.08)^12 = $10,072.68.
P2 = Po(1+r)^n. Compounded quarterly.
r = 8/4 = 2% = quarterly % rate.
n = 4*12 = 48 compounding periods.
P2 = 4000(1+0.02)^48 =
P2-P1 =
To calculate the future value of an investment compounded quarterly, you can use the formula:
Future Value = Principal * (1 + (Rate / n))^(n * t)
Where:
- Principal is the initial investment amount
- Rate is the annual interest rate
- n is the number of times the interest is compounded per year
- t is the number of years the investment is held
In this case, the principal (P) is $4000, the annual interest rate (R) is 8% (or 0.08), the number of times the interest is compounded per year (n) is 4 (quarterly), and the number of years (t) is 12.
To calculate the future value, we substitute these values into the formula:
Future Value = $4000 * (1 + (0.08 / 4))^(4 * 12)
Future Value = $4000 * (1 + 0.02)^48
Future Value = $4000 * (1.02)^48
Using a calculator or a spreadsheet, you can find that (1.02)^48 is approximately 1.7174671.
Future Value = $4000 * 1.7174671
Future Value = $6869.87
Therefore, the future value of Jose's investment would be approximately $6869.87.
To find out how much the investment increased, subtract the initial investment of $4000 from the future value:
Increase = $6869.87 - $4000
Increase ≈ $2869.87
Therefore, the future value of the investment would increase by approximately $2869.87.