## monroe17 3 years ago Miss Crystal Palace just purchased – you guessed it – a crystal palace for \$650,000. She makes a 25% down payment and finances the balance with a mortgage at an interest rate of 5.6% for 15 years, making monthly payments. a. What amount will she borrow? b. Complete the amortization table for the first three payments. (Show all work!)

1. phi

can you answer (a) ? 75% of 650,000 or 650,000- 25% of 650,000

2. monroe17

162500?

3. monroe17

oh wait no. 649999.75?

4. monroe17

no isn't my first answer right?

5. phi

If you put down a down-payment, do you expect it to be all 650,000? to do this, remember that 25% is the same as 25/100 (or 1/4)

6. monroe17

is it 162500?

7. phi

that is the down payment. How much is the loan?

8. monroe17

162500(1+0.056/12)^12*15 162500(1+0.056/12)^180 (162500)(2.311845392)=\$375,674.88

9. monroe17

that's what I did...

10. monroe17

ohh in my equation where i put 162500.. is that supposed to be 487500 instead?

11. phi

162,500 is 1/4 of the 650,000 162,500 is the amount paid up front. You must now borrow the remainder. so your work up above looks good except 162500 is not the correct amount for the loan

12. monroe17

the amount of the loan is 1,127,024.63?

13. phi

For (a), I think they want 487,500 to do (b) you have to figure out how much the total loan ends up costing. Is that the 1,127,024 number?

14. monroe17

yes the total loan I calculated is 1,127,024.63 I believe.

15. phi

now find the monthly payment

16. monroe17

how? what formula?

17. monroe17

6261.25 a month?

18. phi

now you can do the amortization schedule start with the loan balance at the start 487500 add one month of interest (0.056/12)*487500 then subtract off the payment to get the loan balance for the next month. do the same thing for the 2nd (and 3rd) month, except use the new loan principal

19. monroe17

what new loan principal?

20. phi

when you make a payment, the amount you owe goes down

21. monroe17

(0.056/12)*487500= 2275

22. monroe17

487500-2275= 485225 for the next month?

23. monroe17

2264.38--485235.62 2264.43--482971.19

24. monroe17

how do I put that in a chart though with the.. amount of payment interest payment applied to principal and balance?

25. phi

OK, I just checked about loans. there is a formula to figure out the monthly payment FV= payment *( (1+i)^n -1)/i where future value FV is the number you found, does this look familiar?

26. monroe17

yeah, give me a sec.

27. monroe17

so the formula I used gave me 9268.65 as the monthly payment

28. phi

how? I get something else

29. monroe17

P=1127024.63 n=180 r/m=0.56/12=0.0046666667 1127024.63(1+0.0046666667)^180=R[(1+0.0046666667)^180-1)/(0.0046666667)] 2605506.713=R(281.1097278) R=9268.65

30. monroe17

the amount is 1127024.63 the annual rate is 5.6% and the time is 15 years

31. monroe17

and the interest payment is 5259.45

32. phi

I match up, but with 1127024.63=R(281.1097278)

33. monroe17

4009.2 is the applied principal and the balance is 1127024.63

34. monroe17

do I not solve 1127024.63(1+0.0046666667)^180 that?

35. monroe17

because in this example I have is shows to do that..

36. phi

for your formula, it looks like you should use the original loan amount on the left hand side. Do you notice that the left side is future value (1,237,024) which can be calculated as 487500*(1+0.056/12)^180

37. monroe17

ohh so after solving it becomes 1127024.63

38. monroe17

so is the monthly payment 4009.20?

39. phi

yes. so now to the amort. to answer amount of payment interest payment applied to principal and balance? you have the first part. interest is principal* 0.0046666667 (5.6% /12) so you start with P (487500) add interest subtract payment get new P (call it P2 for second month) The interest payment is the amount of interest due. the applied to principal is the amount of the payment left over after paying the interest P2 is the balance

40. monroe17

wait wait.. is the interest payment 5259.45? (1127024.63)(0.0046666667)(1)

41. phi

No, you use Present value (not future value) when you apply the interest.

42. monroe17

(487500)(0.0046666667)(1)=2275.00

43. phi

that looks good. now the payment pays that interest and what is left over pays down the principal

44. monroe17

4009.20-2275.00=1734.20?

45. phi

so now how much is the new principal?

46. monroe17

485765.8?

47. phi

so put those numbers in the first row. now do it again with P=485765.80

48. monroe17

so.. 1734.20*0.0046666667*1?

49. phi

You seem to be missing the main point. you pay interest on the dollars you owe (think of it as rent) after one payment you owe 485765.80. that is what the interest is on (not the 1734)

50. monroe17

2266.91? that is the next interest payment for month 2?

51. phi

yes

52. monroe17

then 1742.29 is the applied principal for month 2?

53. phi

yes

54. monroe17

then the next balance is 484023.51?

55. phi

yes. one more payment to go

56. monroe17

2258.78 for the interest payment?

57. monroe17

and 1750.42 and the applied principal?

58. phi

yes

59. phi

Here is a site that computes the amort http://bretwhissel.net/cgi-bin/amortize

60. monroe17

thank you so much for your help!

61. phi

It helped remind me how to do this stuff. It is a bit complicated.

62. monroe17

haha yeah, well before I had absolute no idea where to start. Thank you so much for helping me..