Match the following statements to the appropriate terms.
The value today of a future amount to be received or paid.
The value at a future date of a given amount invested.
Return on principal plus interest for two or more periods.
Value today of a series of future amounts to be received or paid.
The sum of all the payments or receipts plus the accumulated compound interest on them.
The Correct Answer and Explanation is :
Here are the correct matches for the statements:
- The value today of a future amount to be received or paid — Present Value (PV) Explanation: Present value is the concept that describes how much a future sum of money is worth today, given a specific interest rate (discount rate). Essentially, it’s the reverse of future value. When calculating present value, we discount the future amount by the interest rate over a certain period to determine its value in today’s terms. The formula is: [
PV = \frac{FV}{(1 + r)^n}
] Where FV is the future value, r is the interest rate per period, and n is the number of periods. - The value at a future date of a given amount invested — Future Value (FV) Explanation: Future value refers to the amount of money that an investment will grow to over time, given a specific interest rate. It’s the reverse of present value, as it looks forward into the future and calculates what an initial investment will be worth in the future. The formula is: [
FV = PV \times (1 + r)^n
] Where PV is the present value, r is the interest rate, and n is the number of periods. - Return on principal plus interest for two or more periods — Compound Interest Explanation: Compound interest refers to interest that is calculated on both the initial principal and the accumulated interest from previous periods. The more frequently interest is compounded, the more you will earn or owe. Over multiple periods, compound interest grows exponentially, leading to higher returns or liabilities. The compound interest formula is: [
A = P \times (1 + \frac{r}{n})^{nt}
] Where A is the amount after interest, P is the principal, r is the interest rate, n is the number of times interest is compounded per period, and t is the number of periods. - Value today of a series of future amounts to be received or paid — Present Value of Annuity Explanation: This refers to calculating the value of a series of future cash flows (an annuity) in today’s terms. An annuity involves receiving or paying equal amounts over multiple periods, and the present value of an annuity accounts for the time value of money. The formula for the present value of an annuity is: [
PV = P \times \left( \frac{1 – (1 + r)^{-n}}{r} \right)
] Where P is the periodic payment, r is the interest rate, and n is the number of periods. - The sum of all the payments or receipts plus the accumulated compound interest on them — Future Value of Annuity Explanation: The future value of an annuity is the sum of all payments made in a series, plus the interest accrued on those payments over time. This calculation is useful in determining how much a series of equal payments made today will accumulate to by the end of the investment period. The formula for the future value of an annuity is: [
FV = P \times \left( \frac{(1 + r)^n – 1}{r} \right)
] Where P is the periodic payment, r is the interest rate, and n is the number of periods.