Kevin opened a savings account with Texas National Bank. His account has an APR of 1.95% compounded quarterly. If Kevin opens his account with $2100, how long will it take for the account to earn $10500?

82 years and 3 quarters

Step-by-step explanation:

A = P (1 + r / n) ⁿˣ

P = Principal amount

r = Annual interest rate

n = Number of compounds per year

x = time in years

A = Amount after time 'x'

10500 = 2100 (1 + 0.0195 / 4) ⁴ˣ

Divide the whole equation by 2100

10500 / 2100 = ({2100 (1 + 0.004875) } / 2100) ⁴ˣ

5 = (1.004875) ⁴ˣ

Taking Natural logarithm (㏑) on both sides

㏑ 5 = ㏑ (1.004875) ⁴ˣ

㏑ 5 = 4x ㏑ (1.004875)

1.6094 = 4x (0.004863)

1.6094 = 0.01945x

x = 82.75

So, If compounded quarterly at an APR of 1.95% the amount deposited in savings account of $2100 will accumulate to $10500 in 82 years and 3 quarters.