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If $10 were invested at annual rate of interest of 5% compounded annua
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06 Apr 2023, 03:53
06 Apr 2023, 03:53
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If $10 were invested at annual rate of interest of 5% compounded annually, the total value of investment, in dollars, at the end of 7 years will be?
$10(1.5)7
$10(1.05)7
$70 (1.05)
$10+(0.5)7
$10(1+0.5 × 7)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
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$10(1.5)7
$10(1.05)7
$70 (1.05)
$10+(0.5)7
$10(1+0.5 × 7)
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE SINGLE & COMPOUND INTEREST
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Joined: 20 Feb 2017
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Given Kudos: 1053
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Re: If $10 were invested at annual rate of interest of 5% compounded annua
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13 Apr 2023, 16:52
13 Apr 2023, 16:52
1
Expert Reply
The correct formula for compound interest is given by:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal investment (P) is $10, the annual interest rate (r) is 5% or 0.05 as a decimal, the number of times interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 7.
Plugging in these values into the formula, we get:
A = $10 * (1 + 0.05/1)^(1*7)
A = $10 * (1.05)^7
Using a calculator, we can calculate the value of (1.05)^7, which is approximately 1.4071.
So, the total value of the investment at the end of 7 years (A) is:
A = $10 * 1.4071
A ≈ $14.071
Therefore, the correct answer is $10 * (1.05)^7, which is equivalent to option (b) $10(1.05)^7.
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment/loan, including interest
P = the principal investment/loan amount
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
In this case, the principal investment (P) is $10, the annual interest rate (r) is 5% or 0.05 as a decimal, the number of times interest is compounded per year (n) is 1 (since it is compounded annually), and the number of years (t) is 7.
Plugging in these values into the formula, we get:
A = $10 * (1 + 0.05/1)^(1*7)
A = $10 * (1.05)^7
Using a calculator, we can calculate the value of (1.05)^7, which is approximately 1.4071.
So, the total value of the investment at the end of 7 years (A) is:
A = $10 * 1.4071
A ≈ $14.071
Therefore, the correct answer is $10 * (1.05)^7, which is equivalent to option (b) $10(1.05)^7.
gmatclubot
Re: If $10 were invested at annual rate of interest of 5% compounded annua [#permalink]
13 Apr 2023, 16:52
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