Question

If a nominal interest rate of 8% is compounded continuously, determine the unknown quantity in each of the following situations: a. What uniform EOY amount for 9 years is equivalent to $7,000 at EOY 9? b. What is the present equivalent value of $900 per year for 12 years? c. What is the future equivalent at the end of the fifth year of $237 payments made every six months during the five years? The first payment occurs six months from the present and the last occurs at the end of the fifth year. d. Find the equivalent lump-sum amount at EOY eight when Po $1,100 Click the icon to view the interest and annuity table for continuous compounding when ,-8% per year. a. The uniform EOY amount is S 553. (Round to the nearest dollar.) b. The present equivalent value $900 per year for 12 years is $ 6668. (Round to the nearest dollar.) c. The future equivalent is $ 2867 Round to the nearest dollar.)

Please answer C and D.

Answer 1

Here we calculated the uniform EOY amount. That is, = (A/F, i%, N) = e^r - 1/e^rN - 1 then, = 7,000 (e^0.08 - 1)/e^0.08 times 11 - 1 = 7000 (0.0832)/1.1408 = 7000 (0.05897) = $412.81 (P/A, i, N) = A (e^rN - 1 /e^rN (e^r - 1)) = 900 (e^0.08 times 15 - 1/e^0.08 times 15 (e^0.08 - 1)) = 900 (e^1.2 - 1/e^1.2 (0.0832)) \r\n = 900 (2.3201/0.1930) = 900 (12.0212) = $10,420.18 F/A, I & N) = A (e^rN - 1/e^r - 1) = 233 (e^0.04 times 5 - 1/e^0.04 - 1) = 233 (e^0.2 - 1 /e^0.04 - 1) = 233 (0.2214/0.0408) = 233 (5.4264) = $1,264.35 \r\n Here we find out equivalent sum amount that is, (F/P, i %, N) = P (e^rN) = 1200 (e^0.08 times 7) = 1200 (e^0.56) = 1200 (1.7506) = $2,100.72