Question

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. How much does Juan owe to the bank today?

Answer 1

Answer:

Step-by-step explanation:

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.

hope it helps

:)

Answer 2

Answer:

1458 dollars is the answer. Hope this helps you! have a great day!!