At what annual compound interest rate will a sum of money double in 14 years?…
2022
At what annual compound interest rate will a sum of money double in 14 years?
Use 21/14 = 1.050.
Answer: B. 5% — CONCEPTFor annual compounding, the amount after n years is A = P(1 + r/100)n, where P is the principal and r is the annual rate in percent. When a sum…
- A.
4%
- B.
5%
- C.
6%
- D.
6.5%
Attempted by 4 students.
Show answer & explanation
Correct answer: B
CONCEPT
For annual compounding, the amount after n years is A = P(1 + r/100)n, where P is the principal and r is the annual rate in percent.
When a sum doubles, A/P = 2; therefore, the n-year compound growth factor must equal 2.
APPLICATION
Let P be the principal and r the annual percentage rate. After 14 years, 2P = P(1 + r/100)14.
Divide by P: 2 = (1 + r/100)14.
Take the 14th root: 21/14 = 1 + r/100.
Use the supplied approximation 21/14 = 1.050: r/100 = 0.050, so r = 5.
CROSS-CHECK
At 5% per annum, the 14-year growth factor is (1.05)14 ≈ 1.980, which is approximately 2. The exact rate is about 5.075%, and the supplied root approximation gives the offered value 5%.
RESULT
The intended annual compound interest rate is 5%.