5. Annuity. How many years will it take for a payment of: a. $590 to grow to 909

Question

5. Annuity. How many years will it take for a payment of:

a. $590 to grow to 9090.91 at a compound rate of 14 percent?

b. $900 to grow to future value of 10,586.21 at a compound rate of 14 percent?

6. Mortgage. (Hint: P/Y=12) What is the payoff on a 30 year, 7% original mortgage of:

a. $550,552 with a payment of 3,744.50 with 12 years remaining?

b. $190788 with a payment of 1,143.87 with 15 years remaining?

7. Stock. What is the required rate of return on a stock with a

a. $0.75 expected dividend and a 34 price with 7% growth?

b. $1.25 expected dividend and a 15 price with 8% growth?

Explanation / Answer

a) FV = $9090.91; Payment per period = $590; Compound rate = 14% = 0.14

FV = PMT * Future value int rate factor

Future value int rate factor = 9090.91/590 = 15.408

Future value of int rate factor for an Annuity = [ (1+i)n - 1 ] / i

[ (1+i)n - 1 ] / i = 15.408

(1 + 0.14)n - 1 = 15.408 * 0.14

(1 + 0.14)n = 3.157

Take log base 10 on both sides

n log10 (1.14) = log10 (3.157)

n = 8.774 years

b) FV = $10586.21; Payment per period = $900; Compound rate = 14% = 0.14

FV = PMT * Future value int rate factor

Future value int rate factor = 10586.21/900 = 11.762

Future value of int rate factor for an Annuity = [ (1+i)n - 1 ] / i

[ (1+i)n - 1 ] / i = 11.762

(1 + 0.14)n - 1 = 11.762 * 0.14

(1 + 0.14)n = 2.647

Take log base 10 on both sides

n log10 (1.14) = log10 (2.647)

n = 7.428 years

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a) Mortgage rate = 7%

effective rate = 7/12% = 0.583%

Remaining payments = 12 x 12 = 144

payment = $3,744.50

Payoff = PV
PV = ($3,744.50) [ 1 - (1 + 0.00583)-144 ) ] / (0.00583) = $364191.4972

b) Mortgage rate = 7%

effective rate = 7/12% = 0.583%

Remaining payments = 15 x 12 = 180

payment = $1143.87

Payoff = PV
PV = ($1143.87) [ 1 - (1 + 0.00583)-180 ) ] / (0.00583) = $127294.0211

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Rate of Return = (Expected Dividend / Stock Price) + Growth

a)Rate of Return = (0.75 / 34) + 0.07 = 0.0921= 9.21%

b)Rate of Return = (1.25 / 15) + 0.08 = 0.1633 = 16.33%

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