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Can someone help me please

$4000 are invested in a bank account at an interest rate of 10 percent per year.


Find the amount in the bank after 7 years if interest is compounded annually.
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Find the amount in the bank after 7 years if interest is compounded quarterly.
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Find the amount in the bank after 7 years if interest is compounded monthly.
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Finally, find the amount in the bank after 7 years if interest is compounded continuously.
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User Kamila
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1 Answer

6 votes

Answer:

To find the amount in the bank after 7 years, we can use the formula:

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

where:

A = the amount in the bank after 7 years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For the given problem:

P = $4000

r = 10% = 0.1

t = 7 years

a) Compounded Annually:

n = 1

A = 4000(1 + 0.1/1)^(1*7) = $7449.36

b) Compounded Quarterly:

n = 4

A = 4000(1 + 0.1/4)^(4*7) = $7650.13

c) Compounded Monthly:

n = 12

A = 4000(1 + 0.1/12)^(12*7) = $7727.27

d) Compounded Continuously:

n → ∞ (as n approaches infinity)

A = Pe^(rt) = 4000e^(0.1*7) = $8193.85

Therefore, the amount in the bank after 7 years increases as the compounding frequency increases. If interest is compounded continuously, the amount in the bank will be the highest.

User Eshlox
by
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