Question

Identify which of the following formulas applies to the future value of a series of payments, with interest compounded when the payments are made. I = Prt S = Pert S = R (1 + i)n − 1 i An = R 1 − (1 + i)−n i S = P(1 + i)n

Answer 1

The correct formula for calculating the future value of a series of payments with compound interest is S = R (1 + i)n − 1 / i. This applies to annuities due where payments are made at the beginning of each period.

Step-by-step explanation:

The question is asking to identify the formula used for calculating the future value of a series of payments, with interest compounded at the time of payments. The correct formula from the provided options is S = R (1 + i)n − 1 / i. This formula is used to calculate the future value of an annuity due, which is a sequence of equal payments made at the beginning of each period.

Compounding interest is the process of earning interest on both the initial principal and the accrued interest from previous periods. To find the compound interest, you would take the future value and subtract the present value of the principal. The future value (FV) can be calculated using the formula FV = Principal × (1 + interest rate)^time.

Answer 2

The formula (S = P(1 + i)^n) is used to calculate the future value of a series of equal payments with interest compounded when the payments are made.

Let's break down the components of the formula:

- (S) represents the future value of the series of payments.

- (P) is the periodic payment or the amount of money paid or received at regular intervals.

- (i) is the interest rate per period, expressed as a decimal.

- (n) is the number of periods or the total number of payments.

When you make a series of equal payments (P) at regular intervals, and these payments are subject to compound interest (compounded at the rate of (i) per period), the future value (S) can be calculated by multiplying each payment by the future value interest factor, which is ((1 + i)^n).

This formula is commonly used in financial calculations, such as determining the future value of a series of regular contributions to a savings account or the future value of loan payments over time.

It helps in understanding how the value of these payments grows over multiple compounding periods.