On August 1,1990, Mr.Talamos borrows 9,500 pesos and agrees to pay the compounded amont on the day he pays the debt. If interest is at the rate of 5 1/2% compounded quarterly, how much must Mr. Talamos pay to discharge his obligation on january 1,2001?
amount=9500(1.055)^t where t=10 5/12 or
t= 10.417
check that
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To calculate the compounded amount of the debt, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A = the compounded amount
P = the principal (initial amount borrowed)
r = the annual interest rate (as a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case:
P = 9,500 pesos
r = 5.5% = 0.055
n = 4 (quarterly compounding means 4 times per year)
t = 2001 - 1990 = 11 years
Plugging in these values into the formula, we get:
A = 9,500(1 + 0.055/4)^(4*11)
= 9,500(1.01375)^(44)
≈ 9,500(1.74685516)
≈ 16,596.12 pesos
Therefore, Mr. Talamos must pay approximately 16,596.12 pesos to discharge his obligation on January 1, 2001.
To calculate the amount Mr. Talamos must pay to discharge his debt, we need to use the compound interest formula. The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal amount (initial loan)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years
Let's break down the given information and use the formula to find the final amount:
Principal amount (loan): P = 9,500 pesos
Annual interest rate: r = 5.5% = 0.055 (converted to decimal)
Compounding frequency: Quarterly, so n = 4 (four quarters in a year)
Time: t = 10 full years from August 1, 1990, to January 1, 2001
Now we can substitute these values into the formula and solve for A:
A = 9,500(1 + 0.055/4)^(4*10)
First, calculate the fraction inside the parentheses: (1 + 0.055/4)
= (1 + 0.01375)
= 1.01375
Now, calculate the exponent: (4 * 10) = 40
A = 9,500(1.01375)^40
Using a calculator, raise 1.01375 to the power of 40, and multiply the result by 9,500:
A ≈ 9,500 * 2.322669312
Calculating the product:
A ≈ 22,066.35946
So, Mr. Talamos must pay approximately 22,066.36 pesos to discharge his obligation on January 1, 2001.