Question

a) Kenny wishes to buy a house for $3,500,000 in 10 years and decides to deposit a fixed amount in an investment account at the end of each year of the coming 10 years. Assume that his investment account earns an average yearly return of 16% over the next 10 years. How much should he deposit every year so that he will have enough money in his investment account to purchase the house at the end of 10 years?

b) Kenny wishes to buy a house for $3,500,000 in 10 years and decides to deposit a fixed amount in an investment account at the beginning of each year of the coming 10 years. Assume that his investment account earns an average yearly return of 16% over the next 10 years. How much should he deposit every year so that he will have enough money in his investment account to purchase the house at the beginning of 10 years?

Answer 1

Question a:

Let P = Annual Deposit

n = 10 years

r = annual return = 16%

FV = Amount required = $3,500,000

Annual Deposit Required = [r * FV] / [(1+r)^n - 1]

= [16% * $3,500,000] / [(1+16%)^10 - 1]

= $560,000 / 3.44143508

= $164,153.791

Therefore, annual deposit at the end of every year to purchase the house at the end of 10 years is $164,153.79

Question b:

Let P = Annual Deposit

n = 10 years

r = annual return = 16%

FV = Amount required = $3,500,000

Annual Deposit Required = [[r * FV] / [(1+r)^n - 1]] / (1+r)

= [[16% * $3,500,000] / [(1+16%)^10 - 1] * (1+16%)]

= [$560,000 / 3.95726469

= $141,511.889

Therefore, annual deposit at the beginning of every year to purchase the house at the end of 10 years is $141,511.89