3. A new college hire has been offered a position with a firm starting at $55,00

Question

3. A new college hire has been offered a position with a firm starting at $55,000.00 per year. The new hire is told that in three years her salary is expected to be S67,375.00 per year. At what average interest rate is her salary projected to increase per year? a. 3% b. 5% c. 7% d. 10% Internal 4. The average price of a home today is $200,000.00. How many years will it take for the home value to double if the average annual increase in value is estimated to be 6% per year? a. 6 b. 12 c. 18 d. 24

Explanation / Answer

Answer 3>

Let the average rate of interest be i

Hence,

67375 = 55000 * (1+i)^3

67375/55000 = (1+i)^3

1.25^1/3 = 1+i

1.069987 – 1 = i

Hence I = 0.069987 = 6.9987% = 7% (approx.) – option c

Answer 4>

Current price (P) = 200000

Let the number of years be n

Final Value = A = 2 * 200000 = 400000

Rate = 6%

Therefore

400000 = 200000 * (1+6%)^n

Which gives us,

2 = 1.06^n

Taking log both sides,

Log2 = n*log1.06 (log base 10)

Therefore,

n = log2/log1.06

n = 11.89 or 12 years (approx.) – option b

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