To calculate the future value of an investment with regular contributions and compound interest, we can use the future value of an ordinary annuity formula:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
Where:
- \(FV\) = future value of the annuity
- \(P\) = payment amount per period (contribution per quarter)
- \(r\) = interest rate per period
- \(n\) = total number of payments
Given:
- Quarterly contribution \(P = 1000\)
- Annual nominal interest rate \(APR = 6.72%\)
- Interest rate per quarter \(r = \frac{6.72}{100} \div 4 = 0.0168\)
- Total time in years = 17
- Total number of quarters \(n = 17 \times 4 = 68\)
Let's substitute these values into the future value formula:
- Calculate \(r\):
\[ r = \frac{6.72}{100} \div 4 = 0.0168 \]
- Calculate \(n\):
\[ n = 17 \times 4 = 68 \]
- Substitute values into the formula:
\[ FV = 1000 \times \frac{(1 + 0.0168)^{68} - 1}{0.0168} \]
- Calculate \((1 + r)^n\):
\[ (1 + 0.0168)^{68} \approx (1.0168)^{68} \approx 3.294084 \]
- Subtract 1:
\[ 3.294084 - 1 = 2.294084 \]
- Calculate \(\frac{(1 + r)^n - 1}{r}\):
\[ \frac{2.294084}{0.0168} \approx 136.906 \]
- Calculate the future value \(FV\):
\[ FV = 1000 \times 136.906 \approx 136906 \]
The future value of the account after 17 years of quarterly contributions of $1,000 at a 6.72% APR with quarterly compounding is approximately $136,906.00.