Question 1193606: How many quarterly payments of ₱15,000 will be necessary to pay off
a debt of ₱175,000 if the interest rate charged is 8% converted
quarterly
Found 2 solutions by yurtman, ikleyn:
Answer by yurtman(42)   (Show Source):
You can put this solution on YOUR website! **1. Determine the Quarterly Interest Rate:**
* Annual Interest Rate: 8%
* Quarterly Interest Rate: 8% / 4 = 2% or 0.02
**2. Calculate the Number of Quarterly Payments**
* **Use a financial calculator or spreadsheet software (like Excel or Google Sheets) to determine the number of payments.**
* **In Excel, you can use the NPER function:**
* `=NPER(rate, pmt, pv, [fv], [type])`
* rate: Quarterly interest rate (0.02)
* pmt: Payment amount (-15,000)
* pv: Present value (175,000)
* fv: Future value (0, as the loan will be fully paid off)
* type: 0 for payments at the end of each period (default)
* This will give you the number of quarterly payments required to repay the loan.
* **Using a financial calculator or spreadsheet, you'll find that it takes approximately 14 quarterly payments to repay the loan.**
**Therefore, 14 quarterly payments of ₱15,000 will be necessary to pay off a debt of ₱175,000 at an 8% annual interest rate compounded quarterly.**
Answer by ikleyn(52765)  (Show Source):
You can put this solution on YOUR website! .
How many quarterly payments of ₱15,000 will be necessary to pay off
a debt of ₱175,000 if the interest rate charged is 8%  compounded quarterly
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Use the standard formula for the quarterly payment for a loan
P =  ,
where L is the loan amount; r =  = 0.02 is the effective quarterly compounding interest rate;
n is the number of payments; P is the quarterly payment.
In this problem P = $15000; r = = 0.02.
Substitute these values into the formula and get for quarterly payment
15000 =  .
In this equation, n is the unknown: we should find n from this equation.
Simplify step by step
 =  ,
0.085714286 = ,
 =  ,
4.2857143 = ,
 =  ,
0.233333333 = ,
 = 1 - 0.233333333,
= 0.766666667,
 = 0.766666667,
1.02^n = 1/0.766666667,
1.02^n = 1.304347826
,
n*log(1.02) = log(1.304347826),
n =  = 13.4.
So, 13 full semi-annual payments should be made of 2,000 each,
and then the last,14-th payment, should be made of the lesser amount.
ANSWER. 13 full semi-annual payments should be made of 2,000 each,
and then the last, 14-th payment, should be made of the lesser amount.
The total number of semi-annual payments is 14.
Solved.
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