Question

Janet wants to invest a sum of money that will grow to $10,000 in five years. How much does she need to put now into an account that pays 4% interest per year, compounded monthly?

Answer 1

She needs to put now $8190.0 into the account

Step-by-step explanation:

The formula of the future value of the compounded monthly interest is

$FV=P(1+\frac{r}{n})^{nt}$ , where

1. FV is the future value

2. P is the money invested

3. r is the annual rate in decimal

4. n is the period of time

5. t is the number of years

Janet wants to invest a sum of money that will grow to $10,000 in five

years, into an account that pays 4% interest per year, compounded

monthly

∵ FV = $10,000

∵ r = (4/100) = 0.04

∵ n = 12 ⇒ compounded monthly

∵ t = 5 years

- Substitute these values in the formula above

∴ $10,000=P(1+\frac{0.04}{12})^{12*5}$

∴ $10,000=P(\frac{301}{300})^{60}$

∴ 10,000 = P(1.220996594)

- Divide both sides by 1.220996594

∴ P = $8190.0

She needs to put now $8190.0 into the account

Learn more:

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Answer 2

Answer:

Janet needs to deposit $ 8190.0  in the account.

Step-by-step explanation:

I'm on PLATO and it's correct