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What is the total amount accumulated after three years if someone invests $1,000 today with a simple annual interest rate of 5 percent? With a compound annual interest rate of 5 percent?

  • a)
    $1,150, $1,103

  • b)
    $1,110, $1,158

  • c)
    $1,150, $1,158

  • d)
    $1,110, $1,103

Correct answer is option 'C'. Can you explain this answer?
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Solution:
Given,
Principal amount (P) = $1,000
Simple annual interest rate = 5%
Compound annual interest rate = 5%

Calculation for simple interest:
Simple interest formula,
SI = (P × R × T) / 100
where,
P = Principal amount
R = Rate of interest
T = Time in years

SI = (1000 × 5 × 3) / 100
SI = $150

Total amount accumulated = Principal amount + Simple interest
Total amount accumulated = $1,000 + $150
Total amount accumulated = $1,150

Calculation for compound interest:
Compound interest formula,
A = P (1 + r/n)^(n*t)
where,
A = Amount
P = Principal amount
r = Rate of interest
n = Number of times interest is compounded per year
t = Time in years

Here, the interest is compounded annually, so
n = 1

Applying the values in the formula,
A = 1000(1 + 0.05/1)^(1*3)
A = $1157.63

Hence, the total amount accumulated after three years if someone invests $1,000 today with a simple annual interest rate of 5 percent is $1,150 and with a compound annual interest rate of 5 percent is $1,158. Therefore, option C is the correct answer.
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What is the total amount accumulated after three years if someone invests $1,000 today with a simple annual interest rate of 5 percent? With a compound annual interest rate of 5 percent?a)$1,150, $1,103b)$1,110, $1,158c)$1,150, $1,158d)$1,110, $1,103Correct answer is option 'C'. Can you explain this answer?
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