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MA.912.FL.3.2: Solve real-world problems involving simple, compound and continuously compounded interest.

1. Earl opens a certificate of deposit with $1,500 that pays 2.75% compounded daily.
Part A: Write an equation to model this situation.
Part B. How much money will be in the account after 1 year?
Part C. How much money will be in the account after 5 years?

User AngerClown
by
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1 Answer

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Part A: The formula for the future value of an investment with compound interest is given by:

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

Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years

For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)

Therefore, the equation to model this situation is:

A = 1500(1 + 0.0275/365)^(365*1)

Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:

A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21

Therefore, the amount of money in the account after 1 year is $1,543.21.

Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:

A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59

Therefore, the amount of money in the account after 5 years is $1,805.59.

User H Dindi
by
8.8k points
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