Question

1. Your spendthrift cousins wants to buy a fancy watch for $425. Instead, you suggest that she buy an inexpensive watch for $25 and save the difference of $400. Your cousin eventually agrees with your idea and invests $400 for 40years in an account earning 9% interest per year. How much will she accumulate in this account after 40 years have passed?

2. 4.Kris borrows money in her senior year to buy a new car. The car dealership allows her to defer payments for 12 months, and Kris makes 36 end-of-month payments thereafter. If the original note(loan) is for $24,000 and interest is ½% per month on the unpaid balance, how much will Kris’ payments be?

3. How much money should be deposited each year for 10 years if you wish to withdraw $3,000 each year for five years, beginning at the end of 15th year? Let i=8% per year.

Answer 1

Answer on Question #73171 - Economics / Other

1. Your spendthrift cousins want to buy a fancy watch for $425. Instead, you suggest that she buy an inexpensive watch for $25 and save the difference of $400. Your cousin eventually agrees with your idea and invests $400 for 40 years in an account earning 9% interest per year. How much will she accumulate in this account after 40 years have passed?

Solution-

Interest Rate (r) = 9%

Principal (P) = $400

Time (n) = 40 years

Accumulated Amount (A) is given by:

$$A = P * (1 + r)^{n}$$ $$A = \$400 * (1 + 9\%)^{40}$$ $$A = \$12,563.77$$

Answer-

She accumulates $12,563.77 in this account after 40 years have passed.

2. Kris borrows money in her senior year to buy a new car. The car dealership allows her to defer payments for 12 months, and Kris makes 36 end-of-month payments thereafter. If the original note (loan) is for $24,000 and interest is ½% per month on the unpaid balance, how much will Kris' payments be?

Solution-

$$F_{12} = \$24,000 * (F/P, \frac{1}{2}\%, 12)$$ $$F_{12} = \$24,000 * (1.0617)$$ $$F_{12} = \$25,480.80$$

A = F₁₂*(A/P, ½%, 36)

A = $25,480.80*(0.0304)

A = $774.62 per month

Answer-

The payment of Kris' per month is $774.62.

3. How much money should be deposited each year for 10 years if you wish to withdraw $3,000 each year for five years, beginning at the end of 15th year? Let i=8% per year.

Solution-

F₁₅ = $3,000*(P/A, 8%, 5)

F₁₅ = $3,000*(3.9927)

F₁₅ = $11,978.10

P₀ = F₁₅ (P/F, 8%, 14)

P₀ = $11,978.10*(0.3405)

P₀ = $4,078.54

A = P₀ (A/P, 8%, 10)

A = $4,078.54*(0.1490)

A = $607.70

Answer-

The money should be deposited $607.70 each year for 10 years if you wish to withdraw $3,000 each year for five years.