Question

i need the answers for the following questions the its steps and work

1/ A lender makes a $100,000 mortgage at 3.5% interest with monthly payments for 15 years. How much principal will be repaid during the first year of the loan?

2/Given the following information on a fixed-rate fully amortizing loan, determine the maximum amount that the lender will be willing to provide to the borrower. Loan Term: 30 years, Monthly Payment: $2,500, Interest Rate: 5% (annual rate compounded monthly

3/An investment that costs $105,000 today is expected to produce the following cash inflows over each of the next five years: $20,000; $25,000; $23,000; $22,000; $21,000. What is the IRR (compounded annually) for this investment?

4/Five years ago, you put $20,000 into an interest-earning account. The interest rate is compounded monthly. Today your deposit is worth $30,000. What is the effective annual interest earned on the account?

5/What should an investor pay for an investment property promising a $200,000 return after 10 years if a 7% annual return (compounded annually) on investment is projected?

6/A borrower would like to finance a property worth $1,000,000 for 30 years at 3% interest. The lender indicates that loan fees (origination and discount points) equal to 3% of the loan amount will be charged upfront to obtain the loan. What is the actual effective interest rate of the loan (annual rate of interest, compounded monthly) if the loan is repaid back in 20 years?

7/A buyer can afford no more than $1,200 per month in payments. The most favorable loan available in the market is a 30-year loan at 5%. What is the maximum affordable house with a 20% down payment?

8/An investor buys a 10 unit rental property for $1,000,000. The investor believes that each unit can provide net cash returns of $2,000 per month for 10 years, at which point it can be sold for $2,750,000. What is the internal rate of return (IRR) on the investment?

9/An investor has an opportunity to invest in a rental property that will provide net cash returns of $2,000 per month for 10 years, at which point it can be sold for $400,000. The investor believes that an annual return of 10% should be earned on the property. How much should be paid for the property?

10/Given the following information on a 30-year fixed-payment fully-amortizing loan, determine the remaining balance that the borrower has at the end of five years. Interest Rate: 4%, Monthly Payment: $3,000

Answer 1

Solution 1:

First, we calculate the monthly payment, P

PV = P (PVIFA @ i, n)

$100,000 = P (PVIFA @ 3.5%/12, 15*12)

$100,000 = P (PVIFA @ 0.2917%, 180)

$100,000 = P [(1.002917^180 - 1)/ (0.002917*1.002917^180)]

$100,000 = P (139.8831)

P = $714.88

Interest on loan = 3.5%/12*$100,000 = $291.67

Principal repaid = $714.88 - $291.67

Principal repaid = $423.22

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Solution 2:

Given that Monthly payment, P = $2,500, Interest rate, i = 6%/12 =0.005 and number of years, n = 30*12 = 360

The maximum amount paid to the borrower, PV is

PV = P (PVIFA @ i, n)

PV = $2,500 (PVIFA @ 0.004167, 360)

PV = $2,500 [(1.004167^360 - 1)/ (0.004167*1.004167^360)]

PV = $2,500 (186.2816)

PV = $465,704.04

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Solution 3:

At IRR, NPV = 0

NPV = -105,000 + 20,000/(1 + IRR) + 25,000/(1 + IRR)^2 + 23,000/(1 + IRR)^3 + 22,000/(1 + IRR)^4 + 21,000/(1 + IRR)^5

0 =  -105,000 + 20,000/(1 + IRR) + 25,000/(1 + IRR)^2 + 23,000/(1 + IRR)^3 + 22,000/(1 + IRR)^4 + 21,000/(1 + IRR)^5

105,000 =  20,000/(1 + IRR) + 25,000/(1 + IRR)^2 + 23,000/(1 + IRR)^3 + 22,000/(1 + IRR)^4 + 21,000/(1 + IRR)^5

Solving for IRR, we get

IRR = 1.89%

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Solution 4:

Given that Present Value, PV = $20,000 and Future Value, FV = $30,000 and number of years, n = 5*12 = 60

The effective annual interest rate, i is calculated as follows

FV = PV (1 + i)^n

$30,000 = $20,000 (1 + i/12)^60

1.5 = (1 + i/12)^60

1 + i/12 = (1.5)^(1/60)

1 + i/12 = 1.00678

i = 0.0814 or 8.14%