If $700 is borrowed at 8% interest, find the amounts due at the end of 2 years if the interest is compounded as follows.
i know how to solve this problem but i don't know what to plug in for n in the formula for finding the amount quarterly and hourly. plz help
hourly????
for quarterly compounding
amount = 700(1 + .08/4)^(2*4) = 820.16
for hourly compounding (????)
amount = 700(1 + .08/(365*24))^(2*365*24)
821.46
To find the amounts due at the end of 2 years, compounded quarterly and hourly, you need to use the appropriate formula for compound interest.
First, let's find the compound amount using quarterly compounding. The formula for compound interest compounded quarterly is:
A = P(1 + r/n)^(nt)
Where:
A = the amount including principal and interest
P = the principal amount (the initial amount borrowed)
r = the annual interest rate (expressed as a decimal)
n = the number of times interest is compounded per year
t = the number of years
For your case, the principal amount (P) is $700, the annual interest rate (r) is 8% or 0.08, and the time period (t) is 2 years. Now, we need to find the appropriate value for 'n' (the number of times interest is compounded per year) for both quarterly and hourly compounding.
To find the value of 'n' for quarterly compounding, we need to consider that interest is compounded four times a year (every quarter). So, n = 4.
Similarly, to find the value of 'n' for hourly compounding, we need to consider the number of times interest is compounded per year at an hourly rate. Since there are 24 hours in a day and 365 days in a year (ignoring leap years), the number of times interest is compounded per year would be 24 * 365 = 8,760. Therefore, n = 8,760 for hourly compounding.
Now, let's calculate the amounts due at the end of 2 years for both quarterly and hourly compounding:
For quarterly compounding:
A = 700(1 + 0.08/4)^(4*2)
A = 700(1.02)^8
A ≈ $815.47 (rounded to two decimal places)
For hourly compounding:
A = 700(1 + 0.08/8760)^(8760*2)
A = 700(1.000009085)^17520
A ≈ $815.65 (rounded to two decimal places)
Therefore, the amounts due at the end of 2 years with interest compounded quarterly and hourly would be approximately $815.47 and $815.65, respectively.