### Home > INT1 > Chapter 10 > Lesson 10.1.2 > Problem10-36

10-36.

Talayna has some money that she wants to put into a savings account and she has two options. One option pays $2$% interest compounded quarterly. Another option pays only $1.5$%, but is compounded monthly. If she wants to deposit the money for $5$ years, which account is better? If she wants to deposit for $25$ years, which account is better?

Review the Math Notes box in section 8.1.4

To solve the $2$% compounded quarterly for five years, first find the quarterly interest.

$\frac{.02}{4}=0.005$

The quarterly multiplier becomes $1.005$.
Now use some convenient amount of money to use as principal, say $$100$. $t(n) = 100 · 1.005^{n}$ Now I'll evaluate the function after $5$ years, or when $n = 20$. $t(20) = 100 · 1.005^{20}$ $t(20) = 110.49$ So this$$100$ will become \$$110.49$ after $5$ years.

Use this method to compare the two options above for the time indicated.