Question

A person deposits​ $1,000 in an account every year for four years​ (Years 1 through​ 4), and withdraws half of the balance of the account at the end of Year 4. They put nothing in the account for two years​ (Years 5 and​ 6), then deposit​ $1,500 in the account every year for four more years​ (Years 7 through​ 10). They withdraw the entire balance of the account at the end of Year 10. The account earns​ 6% interest per year for the entire 10 years.

a. Choose the correct cash flow diagram from the​ person's point of view.

b. How much is withdrawn at the end of Year​ 4?

c. How much is withdrawn at the end of Year​ 10?

Answer 1

Assuming Invest money at the start of the year and withdraw money at the end of year.

Interest rate = 6% per year

Initial deposit = $1,000 from year 1 to 4.

Formula to calculate future value of money invested using compound interest formula = P ( 1 + r ) ⁿ where

P = Amount Invested

r = rate of interest

n = Number of years for which amount is invested

Amount deposited at start of year 1 will become 1,000 ( 1 + 0.06)⁴ = 1,262.47 till end of year 4.

Amount deposited at start of year 2 will become 1,000 ( 1 + 0.06)³ = 1,191,01 till end of year 4.

Amount deposited at start of year 3 will become 1,000 ( 1 + 0.06)² = 1,123.6 till end of year 4.

Amount deposited at start of year 4 will become 1,000 ( 1 + 0.06)¹ = 1,060 till end of year 4.

Total amount in account at the end of year 4 = 1,262.47 + 1,191.01 + 1,123.6 + 1,060 = 4,637.08

Half of it is withdrawed which makes it 2,318.84 in the account.

In year 5 till 10, it will earn rate of interest which will make it 2,318.54 (1 + 0.06)⁶ = 3,288.89

Amount deposited at start of year 7 will become 1,500 ( 1 + 0.06)⁴ = 1,893.71 till end of year 4.

Amount deposited at start of year 8 will become 1,500 ( 1 + 0.06)³ = 1,786.52 till end of year 4.

Amount deposited at start of year 9 will become 1,500 ( 1 + 0.06)² = 1,685.4 ill end of year 4.

Amount deposited at start of year 10 will become 1,500 ( 1 + 0.06)¹ = 1,590 till end of year 4.

Total amount at the end of year 10 = 1,893.71 + 1,786.52 + 1,685.4 + 1,590 + 3.288.89 = 10,244.52

a)

b) $2,318.54 is withdrawn at the end of year 4.

c) $10,244.52 is withdrawn at the end of year 10