Question

Christa's $10 deposit in a bank pays 5% interest compounded annually. She notes that at the end of N years, the balance of her account will be B = 10(1.05)^N. About how many years will it take for her initial deposit to double in value?

a) 14 years
b) 16 years
c) 18 years
d) 20 years

Answer 1

To find the number of years it takes for Christa's deposit to double in value with 5% compounded interest, we solve the equation 20 = 10(1.05)^N. After calculating, we find that N is approximately 14.21 years, so the closest answer choice is 14 years.

Step-by-step explanation:

To determine the number of years it will take for Christa's initial deposit to double in value with an interest rate of 5% compounded annually, we can set up the equation B = 10(1.05)^N. Since we want the balance to double, we are looking for when B = 20 (twice the initial deposit).

We can solve for N with the following steps:

1. Set up the equation with B equal to 20: 20 = 10(1.05)^N.
2. Divide both sides by 10 to isolate the exponential term: 2 = (1.05)^N.
3. Use logarithms to solve for N: N = log(2) / log(1.05).
4. Calculate the value using a calculator to find N ≈ 14.21.

The closest full year greater than 14.21 is 15 years, but since the answer choices are in increments of two, the nearest option provided is (a) 14 years.