Question

Mary Ellen invests $4000 in an account that earns 1.8% annual interest compounded monthly.

How many years will it take for the balance of this account to reach $6000?

Round your answer to the nearest tenth of a year.

Answer 1

Answer:

22.5 years to the nearest tenth.

Step-by-step explanation:

The equation is

6000 = 4000(1 + 0.018/12)^12t     where t = the number of years

(1 + 0.018/12)^12t  = 1.5

1.0015^12t = 1.5

Taking logs:

12t log 1.0015 = log 1.5

12t = log 1.5 / log 1.0015

12t = 270.51

t = 22.54 years.

Answer 2

The number of years it will take the account to reach $ 6000 is = 7 years.

The total amount of money invested (P) = $4000

The interest rate(r) for a month = 1.8%

Therefore interest rate for a year = 1.8 × 12

= 21.6%

Simple interest (I) = $6000

But simple interest(si) =

$\frac{p \times t \times r}{100}$

Therefore, time

$t= \frac{i \times 100}{p \times r}$

$t = \frac{6000 \times 100}{4000 \times 21.6}$

$t = \frac{600000}{86400}$

= 7 years.

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