Suppose you contribute $59 per quarter into a fund that 14.5% annual interest. What is the value of your investment after 11 years?
I will assume that the interest rate is 14.5% per annum compounded quarterly, or else we have a much more complicated calculation
amount = 59( (1 + .145/4)^44 - 1)/(.145/4)
= 59(1.03625^44 - 1)/.03625 = $6170.43
To find the value of your investment after 11 years, you need to calculate the future value of your quarterly contributions with compound interest. Here's how you can do that:
Step 1: Convert the annual interest rate to a quarterly interest rate.
Given that the annual interest rate is 14.5%, you need to convert it into a quarterly interest rate. Since there are four quarters in a year, divide the annual interest rate by 4:
Quarterly Interest Rate = 14.5% / 4 = 3.625%
Step 2: Calculate the number of quarters.
Since you contribute $59 per quarter for 11 years, multiply 11 by 4 to calculate the number of quarters:
Number of Quarters = 11 years * 4 quarters/year = 44 quarters
Step 3: Calculate the future value.
Use the formula for the future value of a series of periodic payments with compound interest:
Future Value = Payment * [(1 + Interest Rate)^Number of Quarters - 1] / Interest Rate
Calculating the future value:
Future Value = $59 * [(1 + 3.625%)^44 - 1] / 3.625%
Future Value ≈ $39.573 * [(1.03625)^44 - 1] / 0.03625
Future Value ≈ $39.573 * [2.9982 - 1] / 0.03625
Future Value ≈ $39.573 * 1.9982 / 0.03625
Future Value ≈ $39.573 * 55.0575
Future Value ≈ $2,174.938
Therefore, the value of your investment after 11 years would be approximately $2,174.94.