Final answer:
The program 'Capital' would involve financial calculations such as converting annual interest rates to monthly and understanding the effects of compound interest on loans and investments. Monthly payments are calculated using annuity formulas, and making additional payments on a loan can reduce overall interest and time.
Step-by-step explanation:
The program identifier 'Capital' refers to finance and investment calculations, which often involve converting annual rates to monthly rates and calculating the impact of compound interest over time. To calculate the monthly payment of a loan, we use the formula for an annuity, where the present value PV equals the regular payment R times the factor [1−(1+i)⁻¹]. For a $300,000 loan at a 6% annual interest rate convertible monthly over 30 years, the monthly interest rate (i) is 0.5% or 0.005 (6% divided by 12 months). The number of payments (n) is 360 (30 years times 12 months).
Compound interest is a powerful tool for growing savings, as demonstrated by saving $3,000 at a 7% annual rate, resulting in a substantial increase over 40 years. A similar concept applies when making an extra payment on a loan, such as making 13 payments a year instead of 12, which can significantly reduce the time and money spent on the loan.
Key Aspects of Saving and Loan Payment
- Making larger or additional payments on a loan can save time and money.
- Starting to save early and benefiting from compound interest can vastly increase the initial investment.
- The formula for compound interest is important for understanding investment growth over time.