When he was 18,Gerald put $100 into an account at an interest rate of 8 percent.He now has $171.38 in this account.For how many years did Gerald leave this money in his account?
A) 5 years
B) 6 years
C) 7 years
D) 8 years

Question

Quizplus · Accepted Answer

Using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, t is the time in years, and n is the number of times interest is compounded per year, we can solve for t:

171.38 = 100(1 + 0.08/1)^(1*t)

Taking the natural logarithm of both sides:

ln(171.38) = ln(100) + ln(1.08)^t

ln(171.38/100) = t*ln(1.08)

t = ln(171.38/100) / ln(1.08)

t ≈ 6.963, which rounds up to 7. Therefore, Gerald left the money in the account for 7 years.

When He Was 18,Gerald Put $100 into an Account at an Interest