Question

1. You have $12,000 to invest. You need the money in 13 years, and you expect to earn 6% per year. How much will you have in 13 years? 2. Steven needs $180,000 in 10 years for his daughter's education. If he can earn 6.5% per year, how much does he need to invest today?

3. You have $25,000 to invest and you need $80,000 for a down payment and closing costs on a house. If you want to buy the house in 7 years, what rate of interest do you need to earn?
4. You have $13,000 to invest right now and you figure you will need $25,000 to buy a new car. If you can earn 7.5% per year, how long before you can buy the car?
5. Consider the cash flows presented in the table below. What is the value of the cash flows in year 4 if the interest rate is 8 percent compounded annually?
Year Cash Flow
36528
36558
36589
36621
6. Consider the cash flows presented in the table below. What is the present value if the appropriate interest rate is 6 percent compounded annually?
Year Cash Flow
36526
36559
36587
36621
36652
7. What is the present value of $6,000 per year for 11 years if the interest rate is 5.3%?
8. You are going to borrow $550,000 to buy a house. What will your monthly payment be if the annual interest rate is 4.2 percent, and you borrow the money for 30 years?
9. You borrow $50, 000 to be repaid in 4 equal payments at the end of each of the next 4 years. The bank charges 4.8 percent compounded annually. Prepare the loan amortization schedule.

Answer 1

Step-by-step explanation:

Using the formula for compound interest, we have:

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

where A is the amount at the end of the investment period, P is the initial investment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the given values, we get:

A = 12000(1 + 0.06/1)^(1*13) = $24,343.43

Using the formula for present value of a future sum, we have:

PV = FV / (1 + r)^t

where PV is the present value, FV is the future value, r is the interest rate per year, and t is the number of years.

Plugging in the given values, we get:

PV = 180000 / (1 + 0.065)^10 = $94,297.50

Using the formula for future value of a present sum, we have:

FV = PV(1 + r/n)^(nt)

where FV is the future value, PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

We need to find the interest rate that will give us a future value of $80,000 in 7 years, with an initial investment of $25,000. We can use trial and error, or a financial calculator or spreadsheet, to find the interest rate that satisfies this condition.

Plugging in some values, we find that an interest rate of approximately 9.32% will give us a future value of $80,000 in 7 years.

Using the formula for the number of years required to reach a future value, we have:

t = ln(FV/PV) / ln(1 + r/n)

where t is the number of years, FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of times the interest is compounded per year.

Plugging in the given values, we get:

t = ln(25000/13000) / ln(1 + 0.075/1) = 8.29 years.

Therefore, it will take approximately 8.29 years to reach a future value of $25,000 with an initial investment of $13,000 at an annual interest rate of 7.5%.

To find the value of the cash flows in year 4, we need to discount each cash flow to its present value using the formula:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

Then, we sum up the present values of all the cash flows.

PV(Year 1) = 36528 / (1 + 0.08)^1 = $33,800.93 PV(Year 2) = 36558 / (1 + 0.08)^2 = $30,425.55 PV(Year 3) = 36589 / (1 + 0.08)^3 = $27,398.64 PV(Year 4) = 36621 / (1 + 0.08)^4 = $24,689.89

Therefore, the total present value of the cash flows in