William wishes to save enough money to purchase a retirement lake cabin.He is willing to spend $200,000 for the cabin and he can save $20,000 per year and invest the money into an account earning 7.00% per year.If his investments come in the form of equal annual end-of-the-year cash flows and the first cash flow is in exactly one year,how long will it take him to save enough money to buy the lake cabin?
A)Between 7 and 8 years
B)Between 9 and 10 years
C)Between 10 and 11 years
D)Exactly 10 years

Question

Quizplus · Accepted Answer

To solve this, we use the future value of an annuity formula: FV = P * [((1 + r)^n - 1) / r], where FV is the future value ($200,000), P is the annual payment ($20,000), r is the annual interest rate (7% or 0.07), and n is the number of years. Rearranging the formula to solve for n gives us n = log[(FV*r/P)+1] / log(1+r). Plugging in the values gives us n = log[(200,000*0.07/20,000)+1] / log(1.07), which calculates to a value between 7 and 8 years.

William Wishes to Save Enough Money to Purchase a Retirement