Question

william wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% intrest compounded monthly. How much should william put into this account so that he'll have $4000 at the end of two years?

Answer 1

William should put approximately $3605.40 into the account.

Explanation:

To calculate how much William should put into the account to have $4000 at the end of two years, we can use the formula for compound interest:

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

Where:

A is the final amount (in this case $4000).

P is the principal amount (the initial investment we're trying to find).

r is the annual interest rate (5%, or 0.05).

n is the number of times interest is compounded per year (monthly, so 12 times).

t is the number of years (2).

Plugging in the values, we have:

4000 = P(1 + 0.05/12)^(12*2)

Simplifying:

4000 = P(1 + 0.00417)^(24)

Dividing both sides by (1 + 0.00417)^(24):

P = 4000 / (1 + 0.00417)^(24)

Calculating:

P ≈ 4000 / (1.00417)^(24)

P ≈ 4000 / 1.10944

P ≈ 3605.40

Therefore, William should put approximately $3605.40 into the account.