Exercise 2-4: Present value and future value I. You have invested Sl in your acc

Question

Exercise 2-4: Present value and future value I. You have invested Sl in your account with an interest rate of 100%. a. b. how much money will you have in your account 20 years late How r? many years are required to have $100 in your account? Suppose that there is another investment opportunity with an interest rate of 10% but C. you have invested $1,000, in which year will these two accounts have the same amount of money? 2. You have a bought a house at the price of $500,000. a. If the interest rate is 5%, how many years are required to triple your property value? b. If your property value will be tripled in 15 years, what is the interest rate every year?

Explanation / Answer

QUESTION 1

Part a

This question requires application of time value of money, according to which: FV = PV * (1 + r)n

Substituting, values in question,

FV = $1 * (1 + 100%)20 = $1,048,576 - - > Answer

Part b

This question again requires application of same time value of money function.

100 = 1 * (1 + 100%)n

100 = 2n

Taking natural log on both sides

Ln(100) = n ln(2)

N = 6.64 years - -> Answer

Part c

This question requires equating the two present values, in order to calculate ‘n’.

PV = 1 * (1 + 100%)n ------ first amount

PV = 1000 * (1 + 10%)n ------ second amount

Equating both, in order to calculate n,

1 * (1 + 100%)n = 1000 * (1 + 10%)n

2n = 1000 * (1.1)n

Taking natural log on both sides,

n LN(2) = LN(1000) + n LN(1.1)

n * 0.6931 = 6.9078 + 0.09531 * n

0.5978n = 6.9078

n = 11.55 years - - > Answer

QUESTION 2

Part a

FV = PV * (1 + r)n

3PV = PV * (1 + 5%)n

3 = (1.05)n

LN(3) = n LN(1.05)

N = 22.52 years - -> Answer

Part b

FV = PV * (1 + r)n

3PV = PV * (1 + r)15

3 = (1 + r)15

(1 + r) = 1.07599

r = 7.599% - - > Answer

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