a loan requires that the 4% interest be compounded monthly for 5 years. find the number of compounding periods.
48
60
10
20
________________________________________
Yolanda deposited $11,000 in a savings account that earns 3.5% onterest compounding daily. Find the compound amount after 90 days.
156.89
11,095.34
11,953.34
95.34
#1) how many months in 5 years?
#2) 11000(1+.035/365)^90 = 11095.34
60 months in 5 years?
asd
To find the number of compounding periods for the first question, we need to understand that the loan has an interest rate of 4% compounded monthly for 5 years. The formula to calculate the number of compounding periods is given by the equation:
n = t * m
Where:
n = number of compounding periods
t = duration in years
m = number of compounding periods per year
In this case, the loan duration is 5 years and the interest is compounded monthly. Therefore, the number of compounding periods would be:
n = 5 * 12 = 60
So, the correct answer is 60.
For the second question, we use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = compound amount
P = principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of compounding periods per year
t = time duration in years
In this case, Yolanda deposited $11,000 in a savings account that earns 3.5% interest compounded daily. Therefore, the variables in the formula are:
P = $11,000
r = 3.5% or 0.035 (in decimal form)
n = 365 (since the interest is compounded daily)
t = 90/365 (as the interest is calculated for 90 days)
Now, we can plug in these values and calculate the compound amount (A):
A = 11,000 * (1 + 0.035/365)^(365 * (90/365))
Simplifying the equation:
A = 11,000 * (1 + 0.00009589)^(90)
Calculating the exponent:
A = 11,000 * (1.00009589)^(90)
Finally, we solve for A:
A ≈ 11,095.34
So, the compound amount after 90 days would be approximately $11,095.34, which is the correct answer.