Question

A person invests 3500 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5400 dollars?

Answer 1

10.9 years

Explanation:

Quarterly compounded means that the principal or starting amount earns interest 4 times per year. Accrued means that amount reached, $5,400 in this case. The the variable t represent the time in years.

`t = (ln((Accrued)/(Starting)) )/(4(ln(1+(0.04)/(4)) )`

`t = (ln(5400)/(3500) )/(4(ln(1.01)))`

Put this into a calculator, because it is not at all easy to calculate natural logarithms by hand.

t = 10.895 years

Round to the nearest tenth.

t = 10.9 years