Priestly Engineers wants to save $145,000 to buy some new equipment two years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn a 5.5% rate of return. How much does the firm have to save each quarter to achieve their goal?

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: $FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)$, where $FV$ is the future value ($145,000), $P$ is the payment amount per period (what we're solving for), $r$ is the interest rate per period (5.5% annual rate divided by 4, since interest is compounded quarterly), and $n$ is the total number of payments (2 years * 4 quarters/year = 8 payments). Rearranging the formula to solve for $P$ gives us $P = \frac{FV}{\left( \frac{(1 + r)^n - 1}{r} \right)}$. Plugging in the values: $P = \frac{145,000}{\left( \frac{(1 + 0.055/4)^8 - 1}{0.055/4} \right)}$, we find that $P$ is approximately $17,036.35.

Priestly Engineers Wants to Save $145,000 to Buy Some New