Math Problem Statement

Use MV = P(1 + RT) to find the maturity value (in $) of the loan with a principal of $790,000, rate of 13.35%, and a time period of 9 months.

Solution

The formula provided in the image to calculate the maturity value MVMV of the loan is:

MV=P(1+RT)MV = P(1 + RT)

Where:

  • PP is the principal amount (loan amount),
  • RR is the interest rate per year (expressed as a decimal),
  • TT is the time in years.

Given:

  • Principal P=790,000USDP = 790,000 \, \text{USD},
  • Rate R=13.35%=0.1335R = 13.35\% = 0.1335,
  • Time T=9months=912years=0.75yearsT = 9 \, \text{months} = \frac{9}{12} \, \text{years} = 0.75 \, \text{years}.

Now, let me calculate the maturity value MVMV.The maturity value of the loan is $869,098.75.

Would you like further details or explanations?

Here are 5 related questions to consider:

  1. How would the maturity value change if the loan term was 1 year instead of 9 months?
  2. What would happen if the interest rate increased to 15%?
  3. How can we calculate the interest earned on this loan separately?
  4. What is the relationship between the time and the final maturity value?
  5. How is compound interest calculated differently from simple interest?

Tip: When working with interest rates, always convert percentages to decimals by dividing by 100!