You are planning to retire in 40-years. You plan on putting aside $300 each month and...

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You are planning to retire in 40-years. You plan on puttingaside $300 each month and increase that saving by 0.5% each month.Suppose your investments earn 1% per month, what will youaccumulate after 40 years if you start saving one month from andstop after a last installment in 40 years.
What is the Effective Annual rate for a housing loan at 6% APRwith monthly compounding? What is the APR for a loan when the EARis 6% with monthly compounding?
Compute the outstanding balance on a home mortgage at 4% APR(30 years term at the origination date, and for an original balanceof $100,000, monthly payments) after you have already made paymentsfor 10 years.   What is the principal and interestcomponent of your next payment?
Compute the present value of payments of $300 after 1 year and$500 after 2 years if the rates of interest are 5% and 7% forcorresponding maturities of 1 year and 2 years?
A 10% coupon bond with semi-annual coupon payments, $1000 facevalue matures in 10 years. (a) Compute its price if the YTM is 8%quoted as an APR with semi-annual compounding.   (b) Atwhat YTM will it be a par bond? (c) If the YTM increases to 10%,compute the % change in price.

Compute the price of a zero coupon bond with maturity 30 yearsand par value $1000 and an annual YTM of 12%? If the YTM remainsunchanged what will its price be 20 years from today?
A constant growth stock has the first period dividend at t=1 of$4. If required rate of return is 10% and growth in dividends is5%- (a) compute the price of the stock, (b) its capital gains yieldand its dividend yield? (c) what is the expected stock price in 4years (at t=4)?
A non-constant growth stock pays dividends of $1, $3, $3 and $4in the next 4 years. After the fourth dividend, dividend growthwill be 5%. If the required return on the stock is 10% per year,compute its price today?
A project pays $500 at t=1 and 700 at t=7. Compute the NPV,IRR, Payback period of the project if it costs $700 today. Assumecost of capital is 10% where required.

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a Future Value FV of a growing annuity factor 1rn 1gnrg where r 1 g 05 n number of payments 4012 480 FV factor 11480 1054801 05 1076905 2153805 FV of the growing annuity payment per month FV factor 3002153805 646141629 b Monthly interest rate r 612 05 EAR 1r12 1 10512 1 617 If EAR 6 See Answer

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Transcribed Image Text

You are planning to retire in 40-years. You plan on puttingaside $300 each month and increase that saving by 0.5% each month.Suppose your investments earn 1% per month, what will youaccumulate after 40 years if you start saving one month from andstop after a last installment in 40 years.What is the Effective Annual rate for a housing loan at 6% APRwith monthly compounding? What is the APR for a loan when the EARis 6% with monthly compounding?Compute the outstanding balance on a home mortgage at 4% APR(30 years term at the origination date, and for an original balanceof $100,000, monthly payments) after you have already made paymentsfor 10 years. What is the principal and interestcomponent of your next payment?Compute the present value of payments of $300 after 1 year and$500 after 2 years if the rates of interest are 5% and 7% forcorresponding maturities of 1 year and 2 years?A 10% coupon bond with semi-annual coupon payments, $1000 facevalue matures in 10 years. (a) Compute its price if the YTM is 8%quoted as an APR with semi-annual compounding. (b) Atwhat YTM will it be a par bond? (c) If the YTM increases to 10%,compute the % change in price. Compute the price of a zero coupon bond with maturity 30 yearsand par value $1000 and an annual YTM of 12%? If the YTM remainsunchanged what will its price be 20 years from today?A constant growth stock has the first period dividend at t=1 of$4. If required rate of return is 10% and growth in dividends is5%- (a) compute the price of the stock, (b) its capital gains yieldand its dividend yield? (c) what is the expected stock price in 4years (at t=4)?A non-constant growth stock pays dividends of $1, $3, $3 and $4in the next 4 years. After the fourth dividend, dividend growthwill be 5%. If the required return on the stock is 10% per year,compute its price today?A project pays $500 at t=1 and 700 at t=7. Compute the NPV,IRR, Payback period of the project if it costs $700 today. Assumecost of capital is 10% where required.