Question

Aaron is investing $6,700 of his savings from his summer job. He can choose between simple interest at 6% and compound interest at 5%. Aaron wants to take advantage of the higher interest rate of the simple interest option. At most, for how many years should Aaron invest his summer job savings to gain more with simple interest before compound interest at 5% becomes more financially beneficial?

Answer 1

Aaron will never gain more with simple interest before compound interest becomes more financially beneficial.

A simple interest system computes periodic interest on the principal only. On the other hand, a compound interest system computes interest on both the principal and accumulated interest for each period.

Principal = $6,700

Simple interest rate = 6%

Compound interest rate = 5%

To find out how many years Aaron should invest his savings to gain more with simple interest before compound interest becomes more financially beneficial, we can set up the following equation:

Simple Interest = Compound Interest

6700 * 0.06 * t = 6700 * (1 + 0.05)^t

Where t is the number of years.

Now we can solve for t:

0.06t = (1 + 0.05)^t

0.06t = 1.05^t t * log(0.06)

= log(1.05^t) t * log(0.06)

= t * log(1.05) t * (log(0.06) - log(1.05)) = 0

t = 0 / (log(0.06) - log(1.05))

t = 0

Thus, this equation shows that there is no solution where simple interest at 6% will be more financially beneficial than compound interest at 5%.