6 months ago Juan used his credit card for a transaction of 128 dollars. The bank charges a rate of interest of 50% per month compounded monthly
Answers
Answer:
Compound Interest Equation
A = P(1 + r/n)nt
Where:
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Compound Interest Formulas and Calculations:
Calculate Accrued Amount (Principal + Interest)
A = P(1 + r/n)nt
Calculate Principal Amount, solve for P
P = A / (1 + r/n)nt
Calculate rate of interest in decimal, solve for r
r = n[(A/P)1/nt - 1]
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / n[ln(1 + r/n)] = [ ln(A) - ln(P) ] / n[ln(1 + r/n)]
Formulas where n = 1 (compounded once per period or unit t)
Calculate Accrued Amount (Principal + Interest)
A = P(1 + r)t
Calculate Principal Amount, solve for P
P = A / (1 + r)t
Calculate rate of interest in decimal, solve for r
r = (A/P)1/t - 1
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = t = ln(A/P) / ln(1 + r) = [ ln(A) - ln(P) ] / ln(1 + r)
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pert
Calculate Principal Amount, solve for P
P = A / ert
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
Example Calculation
I have an investment account that increased from $30,000 to $33,000 over 30 months. If my local bank offers savings account with daily compounding (365), what annual interest rate do I need to get from them to match the return I got from my investment account?
In the calculator select "Calculate Rate (R)". The equation the calculator will use is: r = n[(A/P)1/nt - 1] and R = r*100.
Enter:
Total P+I (A): $33,000
Principal (P): $30,000
Compound (n): Daily (365)
Time (t in years): 2.5 years (2.5 years is 30 months)
Your Answer: R = 3.8126% per year
Interpretation: You will need to put $30,000 into a savings account that pays a rate of 3.8126% per year and compounds interest daily in order to get the same return as your investment account.
Step-by-step explanation:
Answer:
the answer is 1458 dollars.
that means, Juan owes 1458 dollars to the bank today.