Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month)?

The concept of compounded interest involves an initial capital that is reinvested month by month, it means that the initial capital plus the interest earned during the first month is reinvested on the second month and so on. The equation that describes the relationship between the final capital with the initial capital, the percentage of compounded interest and the time is:

Cf = Ci(1 + r)^n

where Cf: final capital (the money tha Shorty needs, $142)

Ci: initial capital (the money that Shorty has, $80)

r is the interest (9% = 0,09)

n: time (in months)

⇒142 = 80 (1 + 0,09)^n ⇒ 142/80 = (1,09)^n ⇒ 1.775 = (1,09)^n At this point you have to apply logarithms.

⇒ log (1.775) = n log (1.09) ⇒ n = log (1.775)/log (1.09) ⇒ n= 6.658

Shorty has $142 after 7 month.