## Thursday, March 19, 2020

### Problem-set Essays - Mathematical Finance, Actuarial Science

Problem-set Essays - Mathematical Finance, Actuarial Science 1. Three teachers have different accounts in the same bank. Use the information given below about each teacher to find the missing variable. Mr. Draft: Invested \$450 in savings plan A with annual interest rate 11.4%. After time, he ended up with a total of \$629.55 in her account. How long did he invest? Mr. Callahan: Invested in savings plan B and earned \$25.26 in interest on her investment of \$867.26. He started his investment in January and ended it in June. What was his interest rate? Fr. Moeller: Invested in savings plan C with an annual interest rate of 12%. After two years she earned \$124.50 in interest. How much did she invest? Answer the question asked for each teacher. 2. On a credit card you charge \$200 with an annual interest rate of 15%. Find the amount of interest that you owe if it takes you the following times to pay the credit card. 6 months: 1 year: 2 years: 5 years: 10 years: 20 years: What happens as you take longer and longer to pay off your bill? 3. Accumulate P20,500 for 110 days at 11.5% simple interest 4. What is the principal invested at 8.125% simple interest on May 21, 2007 that will amount to 14,615 on November 18, 2007? 5. Accumulate P15,800 for 4 years and 9 months at 6.875% simple discount. 6. Discount P16, 400 for 5 years and 3 months at 9.875% simple discount. 7. If 25,000 accumulates to 26,700 in 2.5 years, find the (a) interest rate (b) discount rate A 4 month note dated July 4, 2004 with face value of P25,000 bears interest at 13.6%. The note is discounted on September 13, 2004 at a bank whose discount rate is 12.375%. Find the proceeds. 8. How long will it take P4,500 to amount to P6,100; if interest rate is compounded quarterly. 9. How long will it take for P7,350 to amount to P18,500, if invested at 8% compounded monthly? 10. If P3,050 accumulates to P8,660 in 5 years. What is the interest rate compounded monthly? 11. Find the rate compounded quarterly if P745 accumulates P786 in 3 years and 9 months. 12. What nominal rate compounded monthly, will yeild the effective rate 4%? 13. If interest is compounded quarterly find the nominal rate if thge effective rate is 9% 14. Find the effective rate corresponding to the rate 5% compounded quarterly 15. When interest is compounded monthly, find the effective rate corresponding to the nominal rate 3% 16. Find the compound amount and compound interest on principal P20,000 borrowed at 6% compounded annually for 3 years. 17. Find the compound amount, which would be obtained from an interest of P2000 at 6% compounded quarterly for 5 years 18. Find compound interest on P2500 invested at 6% per annually, compound semi-annually for 8 years. 19. Find the interest using the four methods on P8,000 at 11.5% interest from August 2, 2006 to Novemeber 27,2006. 20. Find the interest on P12,000 at 9.875% from NOvember 20,2007 to April 6, 2008.