Question

Kloh put $3000 dollars in a savings account that earns 4% annually, compounded monthly. use logarithms to find how long would it would take for her to double her money?​

Answer 1

`17.4\ years`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=?\ years\\ P=\$3,000\\ r=0.04\\n=12\\ A=\$6,000`

substitute in the formula above

`\$6,000=\$3,000(1+(0.04)/(12))^(12t)`

`2=((12.04)/(12))^(12t)`

Applying log both sides

`log(2)=log[((12.04)/(12))^(12t)]`

`log(2)=(12t)log[((12.04)/(12))]`

`t=log(2)/[(12)log((12.04)/(12))]=17.4\ years`