# theory of interest problem.

• Jun 23rd 2012, 06:08 PM
blakespat
theory of interest problem.
Craig borrows 4500 dollars a year to pay for college expenses, starting on September 1, 2000 - the day he starts college - and ending on September 1, 2004. (i.e. that's 5 withdrawals total). After graduation, he decides to go to graduate school in mathematics, and his loans are deferred (i.e. they still accrue interest, but no payments are due). After graduation from graduate school, he needs to begin paying off his loans. He will make monthly payments for 6 years, and each payment will increase by 1.4 percent. His payments will begin on July 1, 2007, exactly 6 years and 10 months after he started college. If he pays a nominal rate of 6.6 percent convertible monthly for the entire life of the loans, what will be the size of his first payment?

i tried converting the rate to a annual rate and calculated the value of the borrowed money at year 5 then i accumulated for 2yrs and 10/12.. THEN i found the value of the geometrics "annuity" 1 period before the 1st payment and accumulated for 1 month (because i used the monthly interest rate). AND I M STILL GETTING THE WRONG ANSWER!
• Jun 23rd 2012, 06:27 PM
HallsofIvy
Re: theory of interest problem.
6.6 is annual interest rate. Surely no intelligent person is going to pay 6.6*12= 79.2% annual interest!
• Jun 23rd 2012, 07:25 PM
blakespat
Re: theory of interest problem.
i meant i calculated the effective rate j: (1+i/12)^12= 1+j ?? or is it unecessary?
• Jun 24th 2012, 02:57 AM
Wilmer
Re: theory of interest problem.
Code:

```DATE      PAYMENTS      LOANS      INTEREST      BALANCE Aug31/99                                              .00 Aug31/00                4500.00          .00      4500.00 Aug31/01                4500.00      306.15      9306.15 ... Aug31/04                4500.00      1355.34      25776.98 [1] May31/06                            3146.83      28923.81 [2] Jun30/06  -374.14 [3]                159.08      28708.75 Jul31/06  -379.38                    157.90      28487.27 Aug31/06  -384.69                    156.68      28259.26 ... May31/12  -837.98                      9.21        845.07 Jun30/12  -849.72                      4.65          .00```
[1]: owing on day of last loan advance
[2]: owing at month-end previous to 1st payment
[3]: 1st payment (which increases 1.14% monthly)

Any questions?
• Jun 24th 2012, 11:47 AM
blakespat
Re: theory of interest problem.
i tried that! but apparently it s wrong!
• Jun 24th 2012, 01:24 PM
Wilmer
Re: theory of interest problem.
Whoops...I used 60 months instead of 72 months; 1st payment should be 295.04991...
Code:

```DATE      PAYMENTS      LOANS      INTEREST      BALANCE Aug31/99                                              .00 Aug31/00                4500.00          .00      4500.00 Aug31/01                4500.00      306.15      9306.15 ... Aug31/04                4500.00      1355.34      25776.98 [1] May31/06                            3146.83      28923.81 [2] Jun30/06  -295.05 [3]                159.08      28787.84 Jul31/06  -299.18                    158.33      28646.99 Aug31/06  -303.37                    157.56      28501.18 ... May31/12  -780.22                      8.58        787.41 Jun30/12  -791.75                      4.34          .00```
To make up for my goof(!), I'll give you the breakdown:

Step 1: calculate [1]
you need the effective annual rate, since transactions are annual:
i = (1 + .066/12)^12 - 1 = .068033... ; n = 5 (years)
[1] = 4500[(1 + i)^n - 1] / i = 25776.97721...

Step 2: calculate [2]
now we use the equivalent monthly rate:
i = .066 / 12 = .0055 ; n = 21 (months): Sep/04 to May/06
[2] = [1] * (1 + i)^n = 28923.81408...

Step 3: calculate [3] (the first monthly payment)
i remains same (since payments are monthly; n = 72 (6 years)
[3] = [2] * (i - .014) / [1 - (1.014 / (1 + i))^n] = 295.04991...