Question

A house and lot was offered for P87,000 with a 10% down payment and a monthly payment of P500 per month for 25 years. What is the monthly interest rate and the effective rate?

The average annual cost of damages caused by floods to a certain subdivision located along the Pasig River is estimated at P700,000. To build a gravity dam to protect the area from floods would cost P2,500,000 and would involve an annual maintenance cost of P20,000. With the interest at 8% compounded annually, how many years will it take for the dam to pay for itself?

A man wishes to have P35,000 when he retires 15 years from now. If he can expect to receive 4% annual interest, how much must he set aside beginning at the end of each of the 15 years?

Answer 1

a) Price of the house = 87000
Loan Amount = 87000 * ( 1 - 0.1 ) = 78300
EMI = 500
Duration = 25 Years

The PW of the loan is 78300 and EMI is 500 while the duration of that loan is 300 months.
The interest rate can be calculated by the trial and error method using the software.
If we take 1% as monthly interest rate then
=PMT(1%,300,-78300)
= 824.67
That is higher than our value of 500

We will take 0.25% as monthly interest rate
=PMT(0.25%,300,-78300)
= 371.31
This is lower than our value. So the actual interest rate must be between 1% and 0.25% monthly.
We will try 0.5% as a monthly interest rate
=PMT(0.5%,300,-78300)
= 504.49

This is quite close to our value and further trials can give us an exact answer.
=PMT(0.4922%,300,-78300)
= 500.02
The monthly interest is 0.4922%

Effective interest rate = ( 1+ 0.004922 ) ^ 12
= 1.060
( 1.06 -1 ) * 100 = 6%

b) The initial cost is -2500000.
Net Annual Benefits = ( 700000 - 20000 )
= 680000
PV = Cashflow / (1+Discount Rate)^Year
We will create a table for those values considering 10 year period

Year	Cash Flow	PV @ 8%	Cumulative
0	-2500000	-2500000	-2500000
1	680000	629629.6	-1870370
2	680000	582990.4	-1287380
3	680000	539805.9	-747574
4	680000	499820.3	-247754
5	680000	462796.6	215043
6	680000	428515.3	643558
7	680000	396773.5	1040332
8	680000	367382.8	1407714
9	680000	340169.3	1747884
10	680000	314971.6	2062855

The cumulative cash flow has turned positive in the 5th year so the value lies between 4th and 5th year.
247754 / ( 247754 + 215043 ) = 0.54

4 + 0.54 = 4.54 Years

c) The man needs P35000 after 15 years and the interest rate is 4%.
FV of the series of payments is 35000 at a 4% interest rate.
If the payment is made at the end of each period

=PMT(4%,15,,-35000)
= 1747.94