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Sagot :
The annuity that should be worth after 6 years is $63,900.
Given that,
- The present value is $4,500.
- The semi-annual time period should be = 6 × 2 = 12.
- The rate of interest on semi-annual basis should be = 6% ÷ 2 = 3%
Now the following formula should be used:
[tex]Amount = Present\ value \times \frac{(1+ rate)^{(n)} - 1} {rate}\\\\= \$4,500 \times \frac{(1+0.03)^{12} - 1}{0.03}\\\\= \$4,500 \times \frac{0.4257}{0.03}\\\\= \$4,500 \times 14.1920\\\\= \$63,864\\\\= \$63,900[/tex]
Therefore we can conclude that the annuity that should be worth after 6 years is $63,900.
Learn more about the annuity here: brainly.com/question/17096402
Answer: 63900
Step-by-step explanation: Use the savings annuity formula
PN=d((1+r/k)N k−1)r/k
to calculate the value of P6. The question states that r=0.06, d=$4,500, k=2 compounding periods per year, and N=6 years. Substitute these values into the formula results in
P6=$4,500 ((1+0.06/2)6⋅2−1)/(0.06/2).
Simplifying, we have P6=$4,500 ((1.03)12−1)/(0.03). Therefore P6=$63,864.13. Our final answer is 63900.
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