Question

Anita deposited $3,000 into an account that earns 5.2% APR, compounded monthly. How many years will it take to double her money?
Answer:
APR

5.20%

n

12

Y

13.358614

PMT

P

$3,000.00

FV

$6,000.00

My question is how do you get this answer?

Answer 1

Answer:

13.46 years

Step-by-step explanation:

To solve this problem we can use the Exponential Growth Formula since we are talking about compounding interest. The Formula is the following

$y = a*(1+\frac{r}{n})^{nt}$

Where:

• y is the total amount after a given time
• a is the initial amount
• r is the interest rate in decimals
• t is the given time
• n is the amount of compounds per year

Now we can plug all the values into the equation and solve for the amount of years.

$6000 = 3000*(1+\frac{0.052}{12})^{12*t}$ ... solve parenthesis

$6000 = 3000*(1.0043)^{12*t}$ .... divide both sides by 3000

$2 = (1.0043)^{12*t}$ ..... turn into logarithmic form

㏒(1.0043)2 = 12 * t  ..... solve logarithmic form

$161.543 = 12*t$ .....divide both sides by 12

$13.46 = t$

We see that it will take Anita 13.46 years to double her money.

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