A certain investment grows at an annual rate of 5%, compounded annually. If the investment was initially $1,000, how much will it be worth after 5 years?
Correct: B
To find the value of the investment after 5 years, used the formula A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount (initial investment), r is the annual interest rate (in decimal), and n is the number of years. The initial investment is $1,000, the annual rate is 5% or 0.05 as a decimal, and the investment is for 5 years. Plugging these values into the formula, we get A = 1000(1 + 0.05)^5 = 1000(1.05)^5. Calculating (1.05)^5 gives approximately 1.276281562, and multiplying this by 1000 gives approximately $1,276.28. Therefore, after rounding to the nearest dollar, the investment will be worth approximately $1,276.