A MAN MADE A LOAN OF PHP 60,000 PAYABLE IN 3 YEARS AT 8% COMPOUNDED QUARTERLY WHAT IS THE PERIODIC INTEREST RATE?

To find the periodic interest rate, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where: A = the final amount (loan amount + interest) P = the principal amount (loan amount) r = the annual interest rate (in decimal form) n = the number of times interest is compounded per year t = the number of years

In this case, the principal amount (P) is PHP 60,000, the annual interest rate (r) is 8% (or 0.08 in decimal form), the loan is payable in 3 years (t), and the interest is compounded quarterly (n = 4).

We can rearrange the formula to solve for the periodic interest rate (r/n):

(r/n) = (A/P)^(1/(nt)) - 1

Substituting the given values:

(r/n) = (60,000(1 + 0.08/4)^(43))^(1/(43)) - 1

Simplifying the equation:

(r/n) = (60,000(1 + 0.02)^12)^(1/12) - 1

(r/n) = (60,000(1.02)^12)^(1/12) - 1

(r/n) = (60,000(1.268241))^(1/12) - 1

(r/n) = (76,694.46)^(1/12) - 1

Using a calculator, we can find the 12th root of 76,694.46:

(r/n) = 1.006666 - 1

(r/n) = 0.006666

Therefore, the periodic interest rate is 0.006666 or 0.6666%.