Question

An engineer borrowed 50,000 pesos from Social Security System, in the form of calamity loan, with interest at 8% compounded quarterly payable in equal quarterly installments for ten years starting at the end of the first period. Find the quarterly payments.

Answer 1

Answer:

In the given question, the engineer has borrowed 50,000 pesos which is nothing but present value. Also, the interest rate is 8% compounded quarterly payable in quarterly installments for 10 years.Therefore, the given question can be answered using present value of annuity formula.

Also, as the quarterly payments start at the end of the first period, it is a case of annuity regular.

Now, the formula for present value of annuity regular is:

PV = PMT (4- utin i Where PV = Present value of Annuity PMT = Periodic payment i = Interest rate factor = number of compounding periods. n

We have Present value = 50,000 pesos

i = (8/100)/4 = 8/400 = 0.02 ; 1+i = 1.02

n = 10 years x 4 quarters per year = 10 x 4 = 40

Only PMT is missing. So we can find it by substituting remaining available information.

Substituting the above info in the formula, we have:

50,000 = PMT [1-(1/1.02)^40] / 0.02

50,000 = PMT [1-0.45289041523]/0.02

50,000 = PMT [0.54710958477] / 0.02

PMT = 50,000 x 0.02 / 0.54710958477

PMT = 1827.78739001

PMT = 1827.79 pesos (rounded off to 2 decimals)

Therefore, quarterly payment of 1827.79 pesos has to be made for the loan availed.

Alternate method:

You can also use the formula:

Present value = Annuity x PVAF(i,n)

Where, present value = present value of annuity

Annuity = periodic payment

i = Interest per compounding period

n= Number of compounding periods

PVAF(i,n) = present value annuity factor for given i and n

Here i = 8/4 = 2% as the interest is compounded quarterly,

n = 10 x 4 = 40

You can find PVAF from annuity tables and substitute the info and find Annuity amount which is nothing but the quarterly installment

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