Question

The formula A = P(1 + r/n)^nt is used to compute the amount, A, of an initial investment, P, compounded times a year at interest rate, r, after t years. Which expression represents the exponent?

a. r/n
b. t
c. nt
d. P

Answer 1

In the compound interest formula A = P(1 + r/n)^nt, the exponent is represented by nt, which is the frequency of compounding (n) multiplied by the number of years (t).

Step-by-step explanation:

The formula A = P(1 + r/n)^nt is used to calculate the future value A of an initial investment P with an interest rate r compounded n times per year after t years. In this formula, the exponent represents the power to which the term (1 + r/n) is raised, and is given by the expression nt. This exponent reflects the number of times interest is compounded over the total number of years.

Examples:

• If an investment has a 2% interest rate (r = 0.02 for small values of p) compounded annually (n = 1) for 5 years (t = 5), then the exponent is 1*5 or simply 5. The amount after 5 years would be A = P(1 + 0.02)^5.
• Using the rule of 70 as a comparison, we can understand that the time required for an amount to double at a certain interest rate can be inferred from this compounding formula as well.