1. Mathematics of Finance MATH104 Dr. Quinn

2. Your name and picture here Your name Major Brief bio The best projects will be displayed (with your permission) on the new 60+” big screen TV in the lobby of Ross Hall next semester.

3. Example: I take a $10,000 cash advance on my credit card. The card charges 24% interest I make equal payments for 20 years How much interest will I pay? Monthly payment = PMT= = $201.74 Total repaid=($201.74)(12)(20) = $48,417.80 Total interest paid =$48,417.80 - $10,000 = $38,417.80

4. rate24% time20 total interest$38,417.80 debt10,000 PMT$201.74 monthpayto Ito Pnew balancetotal I $10,000.00 1$201.74200.00$1.74$9,998.26$200.00 2$201.74199.97$1.78$9,996.48$399.97 3$201.74199.93$1.81$9,994.67$599.89 4$201.74199.89$1.85$9,992.83$799.79 5$201.74199.86$1.88$9,990.94$999.64 6$201.74199.82$1.92$9,989.02$1,199.46 You can see in the amortization table that only $1.74 of my $201.74 monthly payment goes to pay off the principal the first month. After 240 months of payments, I will have spent $38,417.80 in interest on this $10,000 loan!

5. To pay less interest, we could: Reduce the time on the loan Reduce the interest rate Pay more down Make extra payments towards principal

6. If we reduce the time from 20 years to 10 years Monthly payment = PMT= = $220.48 Total repaid =($220.48)(12)(10) = $26,457.72 Total interest paid =$26,457.72 - $10,000 = $16,457.72 We will pay $18.74 a month, but we will save $38,417.80 – $16,457.72= $21,960.08 in interest!

7. rate24% time10 total interest$16,457.72 debt10,000 PMT$220.48 monthpayto Ito Pnew balancetotal I $10,000.00 1$220.48200.00$20.48$9,979.52$200.00 2$220.48199.59$20.89$9,958.63$399.59 3$220.48199.17$21.31$9,937.32$598.76 4$220.48198.75$21.73$9,915.59$797.51 5$220.48198.31$22.17$9,893.42$995.82 6$220.48197.87$22.61$9,870.80$1,193.69 In the original example, $1.74 went towards principal. Now, by paying it off faster, $20.48 goes towards principal. We will pay $18.74 more a month, but we will save $38,417.80 – $16,457.72= $21,960.08 in interest!

8. If we reduce the rate from r=24% to r=12% Monthly payment = PMT= = $110.11 Total repaid =($110.11)(12)(20) = $26,426.07 Total interest paid=$26,426.07 - $10,000 = $16,426.07 Our monthly payment goes down $91.63 and we save $38,417.80 – $16,426.07= $21,991.73 in interest!

9. rate12% time20 total interest$16,426.07 debt10,000 PMT$110.11 monthpayto Ito Pnew balancetotal I $10,000.00 1$110.11100.00$10.11$9,989.89$100.00 2$110.1199.90$10.21$9,979.68$199.90 3$110.1199.80$10.31$9,969.37$299.70 4$110.1199.69$10.41$9,958.95$399.39 5$110.1199.59$10.52$9,948.44$498.98 6$110.1199.48$10.62$9,937.81$598.46 Our monthly payment goes down $91.63 and we save $38,417.80 – $16,426.07= $21,991.73 in interest!

10. To save the most on interest, we could pay it off in less time (10 years) and at a lower rate (r=12%) Monthly payment = PMT= = $143.47 Total repaid =($143.47)(12)(10) = $17,216.51 Total interest paid=$17,216.51 - $10,000 = $7,216.51 Adjusting both our time and rate makes our monthly payment go down $58.27, and we save $38,417.80 – $7,216.51= $31,200.57 in interest!

11. rate12% time10 total interest$7,216.51 debt10,000 PMT$143.47 monthpayto Ito Pnew balancetotal I $10,000.00 1$143.47100.00$43.47$9,956.53$100.00 2$143.4799.57$43.91$9,912.62$199.57 3$143.4799.13$44.34$9,868.28$298.69 4$143.4798.68$44.79$9,823.49$397.37 5$143.4798.23$45.24$9,778.25$495.61 6$143.4797.78$45.69$9,732.57$593.39 Adjusting both our time and rate makes our monthly payment go down $58.27, and we save $38,417.80 – $7,216.51= $31,200.57 in interest!

12. Conclusion To save interest on a loan: Reduce the rate Reduce the time Pay more down Make extra payments