Making a polar plot (describing the radiation pattern of an antenna)
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Mortgage calculation with SAGE
- PMT: Payment
- PV: Present Value (loan’s principal, amount barrowed)
- r: monthly interest rate (compounded monthly)
- t: number of years of the loan
- m: 12 (compounding period)
- i: r/m=r/12 (intereset rate per compounding period)
- n: mt=12*t (loan’s term, number of monthly payments)
PMT(PV, i, n) = (PV*i)/(1-(1+i)^(-n))
PMT(PV, r, t) = (PVr/12)/(1-(1+r/12)^(-12t))
or with building functions on top of functions
PMT1(PV, r, t) = PMT(PV, i=r/12, n=12*t)
Example: 200,000 USD for a 30-year mortgage at 6.5% compounded monthly PMT(200000, 0.065, 30)
Compounded interest calculation with SAGE
Suppose you deposit $5000 in an account that earns 4.5% compounded monthly. You are curious when your total will reach $ 7000. Using the formula A = P(1+i)n, where P is the principal, A is the amount at the end, i is the interest rate per month, and n is the number of compounding periods (number of months), we have
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