To solve this problem step by step, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, Mr. Talamos borrowed 9,500 pesos, the interest rate is 5 1/2% (or 0.055 in decimal form), and interest is compounded quarterly. The loan is for a period of 10 years (from August 1, 1990, to January 1, 2001).
Let's break down the calculation step by step:
Step 1: Convert the annual interest rate to its decimal form.
r = 5 1/2% = 5.5% = 0.055
Step 2: Determine the number of times interest is compounded per year.
In this case, interest is compounded quarterly, so n = 4.
Step 3: Calculate the final amount using the compound interest formula.
A = 9,500(1 + 0.055/4)^(4*10)
A = 9,500(1.01375)^40
At this point, we can use a table/chart to find the value of (1.01375)^40. Start with 1.01375 and raise it to the power of 1, then continue multiplying the result by itself until you reach the desired power of 40. You can use a calculator or a spreadsheet software like Excel for this calculation.
After finding the value of (1.01375)^40, multiply it by the principal amount (9,500 pesos) to find the final amount, A.
I hope these steps help you solve the problem.