Math 142 Study Guide Test 5 – Finance Read the questions carefully. I have shuffled them deliberately. If the problem says simple interest, use the simple interest formulas. If it implies more than one compoundment, then use compound interest. If it implies more than one payment, use annuity. If it implies paying off a loan, use add-on or amortization. 1. What is the simple interest earned on $500 at 4.3% for 4 years? 2. What is the simple interest future value of $700 at 5% for 20 months? 3. Daytona Dave saves $50 every month at 4.7% compounded monthly, for 10 years. What is his account’s future value? 4. What did Daytona Dave personally contribute in problem 4? 5. What interest did he earn in problem 4? 6. You purchase a motorcycle for $9,000 at 7.9% APR compounded monthly for 5 years. Find your monthly payment. 7. How much money do you need now so that it earns $120 simple interest in 6 months at 3.75%? 8. You inherit $50,000 from crazy Aunt Millicent, but it goes into a trust, where it earns 5.25% interest compounded quarterly, for 7 years. Then you can have the money. How much will you get? 9. Ken wants to save up $12,000 for grad school in 3 years. He opens a sinking fund at 5.3% APR compounded monthly. What should his monthly payment be? 10. What interest will Ken earn in problem 9? 11. Benny purchases $1,000 in stereo speakers. He finances the purchase with an add-on loan at 7% for 2 years. What is his monthly payment? 12. If Benny puts down $200 and finances the rest via the same add-on loan in problem 11 under the same terms, what is his new monthly payment? 13. You are looking for a house and are willing to pay up to $1,000 per month mortgage payment. You get pre-approved for a loan at 6.1% APR compounded monthly for 30 years. What is the most principal you could finance under these terms? 14. Sue puts $2,000 on her credit card at 17% APR compounded monthly for a 10-year term. Determine her monthly payment. 15. Assume Sue makes the minimum payment from problem 14. What portion of that payment went to interest alone? 16. What lump-sum deposit is needed now so that in 7 years it is worth $9,000, assuming 5% APR compounded monthly? 17. What is the interest earned in problem 16? 18. You purchased a government bond for $300. In 9 months, it was redeemed for $325. What was the simple interest rate? 19. Bob bought a jet-ski for $5,000 through an amortized loan at 6% APR compounded monthly for 4 years. What is his monthly payment? 20. Assume Bob makes his monthly payment in problem 19 for one year (12 months). Then he wants to pay off the whole loan at once. What is his unpaid balance? 21. You want to buy an old dirtbike for $400 from your pal. You are willing to pay up to $80 per month for 6 months. If you both agree on an add-on loan, what rate should he charge? 22. You put in $250 per month into a retirement account for 10 years at 4.55% APR compounded monthly. What is the value of this account after 10 years? 23. In problem 22, you then let this sum grow at the same APR and compounding frequency for another 12 years. Find the new future value. 24. Nancy had $2,000 on her credit card on December 1st. On Dec 9th, she paid $300. On Dec 12th, she charged $77. On Dec 20th, she charged $25. What was her average daily balance for December? 25. In problem 24, assume the APR is 12.5%. What is her monthly interest accrued?Answers. (If you think there may be an error, please email me, [email protected]) 1. ܫ = ݎݐ → ܫ = 500ሺ0.043ሻሺ4ሻ= $86 2. ܣ = ܲሺ1+ݎݐሻ→ ܣ = 700൬1+0.05ቀଶଵଶቁ൰ = $758.33. Remember, time in years always. 3. Annuity: ହ൬ቀଵାబ.బరళభమቁభమబିଵ൰ቀబ.బరళభమቁ= $7,640.76. He made regular deposits, hence, it’s an annuity. 4. He made 120 deposits of $50 each, so he made (50)(120) = $6,000 in deposits. 5. Interest = A – P = $7640.76 - $6000 = $1640.76. 6. Amortization: 9000ቀ1+.ଽଵଶቁ=௬௧൬ቀଵାబ.బళవభమቁలబିଵ൰ቀబ.బళవభమቁ→ ݕ݉ݐ = $73.34. 7. ܫ = ݎݐ → 120 = ܲሺ0.0375ሻቀଵଶቁ → ܲ =ଵଶ.ଷହሺ.ହሻ= $6,400. 8. ܣ = 50,000ቀ1+.ହଶହସቁଶ଼→ ܣ = $74,563.97. 9. 12,000 =௬௧൬ቀଵାబ.బఱయభమቁయలିଵ൰ቀబ.బఱయభమቁ→ ݕ݉ݐ = $308.27. Sinking funds are annuities. 10. $308.27 times 36 = $11,097.22. Thus, the difference $12,000 - $11,097.22 = $902.28 interest. 11. Add-on is always simple interest: ܣ = 1000൫1+0.07ሺ2ሻ൯ = $1140÷24 = $47.50 12. Redo it with P = $800: ܣ = 800൫1+0.07ሺ2ሻ൯ = $912÷24 = $38.00. 13. ܲቀ1+.ଵଵଶቁଷ=ଵ൬ቀଵାబ.బలభభమቁయలబିଵ൰ቀబ.బలభభమቁ→ ܲ = 165,017.92. 14. 2000ቀ1+.ଵଵଶቁଵଶ=௬௧൬ቀଵାబ.భళభమቁభమబିଵ൰ቀబ.భళభమቁ→ ݕ݉ݐ = $57.54. 15. ܫ = ݎݐ → ܫ = 2000ሺ0.17ሻቀଵଵଶቁ = $28.33 to interest, the rest to principal. 16. 9000 = ܲቀ1+.ହଵଶቁ଼ସ→ ܲ = $6346.81. 17. I = $9000 - $6346.81 = $2653.19. 18. ܫ = ݎݐ → 25 = 300ሺݎሻቀଽଵଶቁ → ݎ =ଶହଷሺ.ହሻ= 0.11111… = 11.11%. 19. 5000ቀ1+.ଵଶቁସ଼=௬௧൬ቀଵାబ.బలభమቁరఴିଵ൰ቀబ.బలభమቁ→ ݕ݉ݐ = $117.43. 20. ܷ = 5000ቀ1+.ଵଶቁଵଶ−ଵଵ.ସଷ൬ቀଵାబ.బలభమቁభమିଵ൰ቀబ.బలభమቁ= $3,859.82. (elapsed time, T = 1). 21. You’ll pay 80 x 6 = $480, or $80 above the $400 selling price. Add-on loans are simple interest, so use I = prt: 80 = 400ሺݎሻቀଵଶቁ → ݎ =଼ସሺ.ହሻ= 0.4 = 40%. 22. Annuity: ܣ =ଶହ൬ቀଵାబ.బరఱఱభమቁభమబିଵ൰ቀబ.బరఱఱభమቁ= $37,900.07. 23. The sum in problem 22 grows for another 12 years but with no more deposits. This is a compound interest future value: ܣ = 37900.07ቀ1+.ସହହଵଶቁଵସସ= $65,360.65.24. The table will look like this: Date Activity Balance Days 12-1 $2000 8 12-9 -$300 $1700 3 12-12 +$77 $1777 8 12-20 +$25 $1802 12 (thru Dec 31) Be sure your days add up to 31 in this case.
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