Sheetal has made an investment that will pay her $11,455, $16,376, and $19,812 at the end of the next three years. Her investment was to earn her a return of 14 per cent. How much did she invest? (Round to the nearest dollar.)

Question

Quizplus · Accepted Answer

To find out how much Sheetal invested, we need to calculate the present value of the future cash flows ($11,455, $16,376, and $19,812) discounted at the given rate of return (14%). The formula for the present value of a future amount is:$$ PV = \frac{FV}{(1 + r)^n} $$where $PV$ is the present value, $FV$ is the future value, $r$ is the rate of return, and $n$ is the number of periods.For each cash flow, we calculate its present value and sum them up:1. For $11,455 at the end of year 1:$$ PV_1 = \frac{11,455}{(1 + 0.14)^1} = \frac{11,455}{1.14} = 10,044.74 $$2. For $16,376 at the end of year 2:$$ PV_2 = \frac{16,376}{(1 + 0.14)^2} = \frac{16,376}{1.2996} = 12,598.82 $$3. For $19,812 at the end of year 3:$$ PV_3 = \frac{19,812}{(1 + 0.14)^3} = \frac{19,812}{1.4816} = 13,378.44 $$Adding these up:$$ Total \, PV = 10,044.74 + 12,598.82 + 13,378.44 = 36,022 $$Rounded to the nearest dollar, Sheetal invested $36,022.

Sheetal Has Made an Investment That Will Pay Her $11,455