Principles of Finance Math Ch. 4,5, & 7

Compute the future value in year 9 of a $2,000 deposit in year 1, and another $1,500 deposit at the end of year 3 using a 10 percent interest rate.

$2,000×1.1^8+$1,500×1.1^6 = $4,287.18+$2,657.34 = $6,944.52.

A deposit of $350 earns the following interest rates: 8 percent in the first year. 6 percent in the second year. 5.5 percent in the third year. What would be the third year future value?

$350 × 1.08 × 1.06 × 1.055 = 422.72

What is the present value of a $350 payment in one year when the discount rate is 10 percent?

$350 ÷ 1.10 = 318.18 or 315.00

What is the future value of a $900 annuity payment over five years if interest rates are 8 percent?

$900×(1.08^5−1/0.08) = $900×5.8666 = $5,279.94

Determine the interest payment for the following three bonds. (Assume a $1,000 par value.) Corporate zero-coupon bond maturing in 10 years.

0.00

What annual rate of return is earned on a $1,000 investment when it grows to $1,800 in six years?

1000 = 1800/(1+r)^6 (1+r)^6 = 1800/1000 (1.8^1/6 - 1) = 0.1029 or 10.29%

How much would be in your savings account in 11 years after depositing $150 today if the bank pays 8 percent per year?

150*1.08^11=349.75

What is the present value of a $1,500 payment made in nine years when the discount rate is 8 percent?

1500/(1.08)^9 = 750.37

Determine the interest rate earned on a $1,400 deposit when $1,800 is paid back in one year.

1800-1400=400 400/1400=.2857 or 28.57%

What is the future value of $500 deposited for one year earning an 8 percent interest rate annually?

500*1.08=540

Using the Rule of 72, approximately what interest rate is needed to double an investment over five years?

72 ÷ 5 = 14.40

Using the Rule of 72, approximately how many years are needed to double a $100 investment when interest rates are 7 percent per year?

72 ÷ 7 = 10.29

A 6 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond?

Call Price = par value + call premium 1,000 + 60 = 1,060

What's the current yield of a 3.8 percent coupon corporate bond quoted at a price of 102.08?

Current Yield = (Annual Coupon Payment / Current Bond Price) * 100 37.23 = (38/102.08)*100 1.038 * 1,000 = 38

Compute the present value of a $2,000 deposit in year 1, and another $1,500 deposit at the end of year 3 if interest rates are 10 percent.

PV = $2,000 ÷ (1 + 0.10)1+ $1,500 ÷ (1 + 0.10)3= $1,818.18 + $1,126.97 = $2,945.15

Calculate the price of a zero coupon bond that matures in 20 years if the market interest rate is 3.8 percent. Assume semiannual compounding.

PV = FV / (1 + r/n)^(nt) PV = $1000 / (1 + 0.038/2)^(2*20) 463.19

What's the present value, when interest rates are 7.5 percent, of a $50 payment made every year forever?

PV of a perpetuity = $50/0.075 = $666.67

If the present value of an ordinary, 7-year annuity is $6,500 and interest rates are 7.5 percent, what's the present value of the same annuity due?

PVA7 due = $6,500×(1+0.075) = $6,987.50.

Compute the price of a 3.8 percent coupon bond with 15 years left to maturity and a market interest rate of 6.8 percent. (Assume interest payments are semiannual.)

n= 30 I%= 3.4 or 6.8/2 pmt= 19 fv= 1000 Present value is 732.66 Premium bond

What's the present value of a $900 annuity payment over five years if interest rates are 8 percent?

N = 5, I = 8, PMT = −900, FV = 0, CPT PV == 3,593.44

If the future value of an ordinary, 7-year annuity is $6,500 and interest rates are 7.5 percent, what is the future value of the same annuity due?

FVA7 due = $6,500×(1+0.075) = $6,987.50.

Determine the interest payment for the following three bonds. (Assume a $1,000 par value.) 3.5% coupon corporate bond (paid semi-annually)

Interest Payment = (coupon rate / 100) * PV

Determine the interest payment for the following three bonds. (Assume a $1,000 par value.) 4.25% coupon treasury note.

Interest Payment = Coupon Rate x Par Value

You wish to buy a $25,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments? How would the payment differ if you paid interest only?

Monthly Payment: N = 4 × 12, I = 9 ÷ 12, PV = 25,000, FV = 0, CPT PMT = −622.13 Interest Only Payment: 25,000*.09/12 = 187.5 You would still owe the 25,000.