Question

9. When interest is compounded semi-annually, the formula used to find the amount of an investment is $A = P \left(1 + \frac{i}{2}\right)^{2n}$, where A represents the amount, P represents the principal invested, i represents the annual interest rate, as a decimal, and n represents the number of years of the investment. a) Use the formula to determine the amount that each investment would be worth. i) $5000 at an annual rate of 4%, compounded semi-annually, for 10 years ii) $4000 at an annual rate of 5%, compounded semi-annually, for 20 years b) If interest is compounded quarterly, the formula becomes $A = P \left(1 + \frac{i}{4}\right)^{4n}$. Use the formula to determine the amount that the investments from part a) would be worth if they were compounded quarterly. c) Explain the difference in the answers for parts a) and b). Initial Amount: Growth Rate 100% + Period: Time: a) b) c)

Name: 9 when interest is compounded semi annually the formula used to find the amount of an investment is a p left1 fraci2right2n where a represents the amount p represents the principal invested 92046
Uploaded: 2022-06-04T15:53:49-08:00
Duration: 2 min 29 s
Channel: Andrew Noble
Description: 9 when interest is compounded semi annually the formula used to find the amount of an investment is a p left1 fraci2right2n where a represents the amount p represents the principal invested 92046

          9. When interest is compounded semi-annually, the formula used to find the amount of an investment is
$A = P \left(1 + \frac{i}{2}\right)^{2n}$, where A represents the amount, P represents the principal invested, i represents the annual interest rate, as a decimal, and n represents the number of years of the investment.
a) Use the formula to determine the amount that each investment would be worth.
i) $5000 at an annual rate of 4%, compounded semi-annually, for 10 years
ii) $4000 at an annual rate of 5%, compounded semi-annually, for 20 years
b) If interest is compounded quarterly, the formula becomes $A = P \left(1 + \frac{i}{4}\right)^{4n}$. Use the formula to determine the amount that the investments from part a) would be worth if they were compounded quarterly.
c) Explain the difference in the answers for parts a) and b).

Initial Amount: Growth Rate 100% + Period: Time:
a)
b)
c)

$9 when interest is compounded semi annually the formula used to find the amount of an investment is a p left1 fraci2right2n where a represents the amount p represents the principal invested 92046$

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