A person invests 9500 dollars in a bank. The bank pays 5.75% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 12600 dollars?

4.9 years

Step-by-step explanation:

Future value is the sum of amount invested and its compounded interest for a specific period of time and on a specific interest rate.

Investment = Present value = $9,500

Future value = $12,600

To find the numbers of years we will use following formula

Future value = Present value x (1 + r) ^n

r = interest rate = 5.75%

n = number of periods = ?

Placing values in the formula

$12,600 = $9,500 x (1 + 5.75%/4) ^n

$12,600 / $9,500 = 1.014375^n

1.3263 = 1.014375^n

Log 1.3263 = n log 1.014375

n = Log 1.3263 / log 1.014375

n = 19.7856 Quarters

n = 4.9 years