Simple Bank Interest Compound

Algebra Level 3

Theo wants to open a savings account with his newfound $100.

He has a choice:
he can either open it at Cat Bank which offers 10% interest per year compounded annually, or
he can go to the Fish Bank which guarantees 17% simple interest per year.

After how many years will it be more profitable to go to Cat Bank?


The answer is 12.

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A P by A P , 26, USA

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2 solutions

Justin Malme
Jun 4, 2016

P P = principle
r r = annual interest rate
t t = time in years
n n = number of times compounded per year


Compound interest = P ( 1 + r n ) n t P(1+\frac{r}{n})^{nt} = 100 ( 1 + . 1 1 ) 1 t 100(1+\frac{.1}{1})^{1t} = 100 ( 1.1 ) t 100(1.1)^t
Simple interest = P r t + P Prt+P = 100 ( . 17 ) t + 100 100(.17)t+100 = 17 t + 100 17t+100

Set the two equal to each other:
17 t + 100 17t+100 = 100 ( 1.1 ) t 100(1.1)^t ⇒ \Rightarrow 1. 1 t − . 17 t = 1 1.1^t-.17t=1 ⇒ \Rightarrow t = 11.162... t=11.162...

Therefore, 12 years.

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How did you manage to get the value of t t ? I can't find a way to solve the equation

Hung Woei Neoh - 5 years ago

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Seconded. I can't solve this either, please explain?

Ingrid Spangler - 3 years, 1 month ago

100(1+0.1)^x= 100+17x. Solve for x( periods) where both sides of the equation equal to each other.

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