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At the end of each quarter, Patti deposits $1,600 into an account that pays 8% interest compounded quarterly. How much will Patti have in the account in five years?

Multiple Choice

$40,476


$38,876


$46,876


$40,176

User Regality
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1 Answer

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Answer: To calculate the amount Patti will have in the account after five years, we can use the compound interest formula:

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

Where:

A = the final amount in the account after t years

P = the initial principal (the amount deposited at the end of each quarter)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

Given:

P = $1,600 (deposited at the end of each quarter)

r = 8% = 0.08 (converted to decimal form)

n = 4 (compounded quarterly)

t = 5 years

Now, plug in the values into the formula:

A = 1600(1 + 0.08/4)^(4*5)

A = 1600(1 + 0.02)^(20)

A = 1600(1.02)^20

Using a calculator, calculate the value of (1.02)^20:

(1.02)^20 ≈ 1.485946

Now, multiply by $1600:

A ≈ 1600 * 1.485946 ≈ $2,377.51

So, Patti will have approximately $2,377.51 in the account after five years.

None of the multiple-choice options match the calculated value exactly. The closest option is $40,476, but the correct value is $2,377.51.

User Prisma
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