Asked by Linda Cashdollar on May 27, 2024
Verified
Evaluate $20,000[(1+0.052) 4−10.052]\$ 20,000\left[\frac{\left(1+\frac{0.05}{2}\right) ^{4}-1}{\frac{0.05}{2}}\right]$20,000[20.05(1+20.05) 4−1]
A) $172,405.00
B) $82,207.63
C) $83,050.31
D) $41,525.16
E) $86,202.50
Compound Interest
Calculating interest by including both the original principal amount and the interest that has been piled up from former periods.
Exponential Functions
Mathematical functions describing growth or decay at rates proportional to the value of the function at any point in time.
- Make use of financial formulas for determining the future and present worth of investments.
Verified Answer
SS
Simranjit SinghMay 28, 2024
Final Answer :
C
Explanation :
The expression is a formula for the future value of a series of cash flows (like an annuity). The formula is used to calculate the future value of an annuity due to compound interest. Here, the interest rate per period is 0.05/2 = 0.025 (since it's compounded semi-annually), and the number of periods is 4. Plugging these values into the formula gives: $20,000[(1+0.025)4−10.025]\$ 20,000\left[\frac{\left(1+0.025\right)^{4}-1}{0.025}\right]$20,000[0.025(1+0.025)4−1] Calculating the expression inside the brackets first: (1+0.025)4−1=(1.025)4−1≈0.103812890625\left(1+0.025\right)^{4}-1 = (1.025)^4 - 1 ≈ 0.103812890625(1+0.025)4−1=(1.025)4−1≈0.103812890625 Then, dividing by 0.025: 0.1038128906250.025≈4.152515625\frac{0.103812890625}{0.025} ≈ 4.1525156250.0250.103812890625≈4.152515625 Finally, multiplying by \$20,000: $20,000×4.152515625≈$83,050.31\$20,000 \times 4.152515625 ≈ \$83,050.31$20,000×4.152515625≈$83,050.31 Therefore, the correct answer is \$83,050.31, which is option C.
Learning Objectives
- Make use of financial formulas for determining the future and present worth of investments.
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