Question

Olga invests $3000 in an account that earns 1.3% annual interest compounded monthly. How many years will it take for the balance of this account to reach $5000? Enter your answer in the box. Round your answer to the nearest tenth of a year.

Answer 1

It will take 39.3 years for the balance of this account to reach $5000

Step-by-step explanation:

Formula for time (t)

t = $\frac{ln(\frac{A}{P})}{n[ln(1+\frac{r}{n})]}$

Where:

1. A = the value of the accrued investment/loan

2. P = the principal amount

3. r = the annual interest rate (decimal)

4. n = the number of times that interest is compounded per unit t

5. t = the time the money is invested or borrowed  

∵ Olga invests $3000 in an account that earns 1.3% annual interest

   compounded monthly

∴ P = $3000

∴ r = 1.3% = 1.3 ÷ 100 = 0.013 ⇒ annual interest

∴ n = 12 ⇒ compounded monthly

∵ The account will reach $5000

∴ A = 5000

- Substitute these values in the rule above

∴ t = $\frac{ln(\frac{5000}{3000})}{12[ln(1+\frac{0.013}{12})]}$

∴ t = 39.3 years

It will take 39.3 years for the balance of this account to reach $5000

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