Eric borrowed 515 dollars today and has agreed to pay back in equal monthly installments over 6 years. The bank charges Eric 4.94% per year, compounded monthly. What is the amount that Eric will owe the bank at the end of month 20 (that is, after the 20-th installment has been paid)? (Accuracy is set at the second decimal.)
To find the amount that Eric will owe the bank at the end of month 20, we need to use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount after time t
P = the principal amount (in this case, the borrowed amount of 515 dollars)
r = the interest rate per year (4.94%, or 0.0494 expressed as a decimal)
n = the number of times interest is compounded per year (12, since it's compounded monthly)
t = the time in years (20/12, since we are calculating for month 20)
By substituting the values into the formula, we can calculate the amount owed:
A = 515(1 + 0.0494/12)^(12*(20/12))
Calculating this equation gives us the amount that Eric will owe the bank at the end of month 20.