Math Problem Statement

How to calculate monthly payments over the life of a loan or purchase is using the formula attached. Car is $148,250 interest rate is 5.34%

How to calculate monthly payments over the life of a loan or purchase is using the formula attached. Car is $148,250 interest rate is 5.34%

Solution

To calculate the monthly payment using the given formula, let's identify and substitute the values.

The formula is: d=PN(rk)(1+rk)Nk1d = \frac{P_N \left( \frac{r}{k} \right)}{\left( 1 + \frac{r}{k} \right)^{Nk} - 1} where:

  • dd = amount of each monthly deposit (payment),
  • PNP_N = principal or initial loan amount,
  • rr = annual interest rate (as a decimal),
  • kk = number of compounding periods per year (monthly means k=12k = 12),
  • NN = number of years for the loan.

Given values:

  • PN=148,250P_N = 148,250 (cost of the car),
  • r=5.34%=0.0534r = 5.34\% = 0.0534 (annual interest rate in decimal form),
  • k=12k = 12 (monthly compounding),
  • NN = the loan period in years (you'll need to provide this to proceed).

Once we know the term NN, I can substitute all values and compute the monthly payment dd. Could you provide the loan duration in years?

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Math Problem Analysis

Mathematical Concepts

Finance
Compound Interest
Monthly Payments

Formulas

d = (PN * (r/k)) / ((1 + (r/k))^(Nk) - 1)

Theorems

Compound Interest Formula for Loan Payments

Suitable Grade Level

Undergraduate