Question

John plans to buy a vacation home in 11 years from now and wants to have saved $49,349 for a down payment. How much money should he place today in a saving account that earns 9.73 percent per year (compounded daily) to accumulate money for his down payment? Round the answer to two decimal places

Answer 1

This is a problem of compound interest and we will employ the compound interest formula for this question i.e.

A = P*(1+r/n)^(nt) where

A = Amount required after the time period = $49,349

P = Principal to be invested today = We have to find this value

r = Rate of interest = 9.73%

n = number of times interest applied per time period = 365 (As the interest is compounded daily)

t = number of time periods = 11 Years

Therefore P = 49349 / (1+9.73/365)^(365*11)

P = $16,924.46

Hence the amount John needs to invest today to get $ 49,349 after 11 years is $ 16,924.46