Ahmed rents his cabin every day for $$ 175$ . He deposits that money daily into an annuity at $6 %$ compounded continuously.
(a) How much will his annuity be worth after 300 days?
(b) How much of that will be interest?

Round your answers to the nearest dollar and do not use commas in the answer blanks.
(a) $$$
(b) $$$

Answer

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Answer

Round the interest earned to the nearest dollar: $2654$

Steps

Step 1 ：Calculate the total principal amount after 300 days: $P = 175 \times 300 = 52500$

Step 2 ：Convert the time to years: $t = \frac{300}{365} \approx 0.8219$ years

Step 3 ：Use the formula for continuous compounding interest: $A = P e^{r t}$

Step 4 ：Calculate the annuity value after 300 days: $A = 52500 \times e^{0.06 \times 0.8219} \approx 55153.94$

Step 5 ：Round the annuity value to the nearest dollar: $55154$

Step 6 ：Calculate the interest earned: $Interest = A - P = 55153.94 - 52500 \approx 2653.94$

Step 7 ：Round the interest earned to the nearest dollar: $2654$