Question

1. If Joe has $5,600 today and invest it at a 10% interest rate, how much will he have in 12 years?

Answer 1

This is an example of a geometric series, with first term (a) = 5600, number of years n = 12 and common ratio, r = 1.1. Using the formula for the sum of a geometric series
\[a(1-r^n)/(1-r)\]
and substituting in known values gives
\[5600(1-1.1^12)/(1-1.1)\] = 119,751.981 which is about $120,000. Hope this helps.

Answer 2

if it is ten percent per year you want to compute
\[5600\times (1.10)^{12}\] you would use a summation formula if you kept depositing money

Answer 3

I don't think this is feasible. Although the money is being summed, the money does not increase by a fixed amount each year, it increases by a fixed interest rate.

Answer 4

Therefore a geometric series would be more appropriate for this problem than an arithmetic series. The answer to the computation in the last case would be 17575 rather than about 120,000.