Noah is going to put $2,000 in a savings account. He plans on putting the money in an account and leaving it there for 5 years. He can put the money in an account that pays 1% interest monthly, an account that pays 6% interest every six months, or an account that pays 12% interest annually.Which account will give him the most money in his account at the end of the 5 years?
Question
Noah is going to put $2,000 in a savings account. He plans on putting the money in an account and leaving it there for 5 years. He can put the money in an account that pays 1% interest monthly, an account that pays 6% interest every six months, or an account that pays 12% interest annually.Which account will give him the most money in his account at the end of the 5 years?
Solution
To answer this question, we need to understand how compound interest works. Compound interest is calculated on the initial principal, which also includes all of the accumulated interest from previous periods on a deposit or loan.
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If Noah puts his money in an account that pays 1% interest monthly, the interest is compounded 12 times a year. The formula for compound interest is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (in decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
So, A = 2000(1 + 0.01/12)^(12*5) = $2,271.24
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If Noah puts his money in an account that pays 6% interest every six months, the interest is compounded 2 times a year. So, A = 2000(1 + 0.06/2)^(2*5) = $2,683.64
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If Noah puts his money in an account that pays 12% interest annually, the interest is compounded 1 time a year. So, A = 2000(1 + 0.12/1)^(1*5) = $3,532.88
So, the account that will give him the most money at the end of the 5 years is the one that pays 12% interest annually.
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