Thursday, January 05, 2006
installment loans: annuities
Ahhh. I got so caught up in china and banking and real estate and bird flu and indie rock that I haven't posted anything about mathematics in a long time. As this is a Math Blog, let's get to work children.
For those of you with student loans, if you've ever wanted to calculate how much interest you'd pay on your loan over your payment period, I'll go over how. This is simple shit people, things you learned in high school but probably are a little rusty on (unless you are a CPA, broker, etc.).
Say you have 5 $4000 loans that you consolidated back in June at an interest rate of 2.57% to be paid in monthly installments over a 10-year period. Let's first calculate your monthly payment amount.
This type of loan is called an annuity (where you pay off a loan in installments). Here, the principle is $20000 (P), on which you will pay back the lender at an interest rate of 2.57% (i) per year for 10 (n) years, in 12 (q) equal payments per year. The monthly payment M is:
M = Pi/[q(1-[1+(i/q)]-nq)]
Plugging the numbers in we get M = $189.18.
To get the total interest payed over 10 years on this loan, calculate Mnq - P, which is $2701.60.
For those of you with student loans, if you've ever wanted to calculate how much interest you'd pay on your loan over your payment period, I'll go over how. This is simple shit people, things you learned in high school but probably are a little rusty on (unless you are a CPA, broker, etc.).
Say you have 5 $4000 loans that you consolidated back in June at an interest rate of 2.57% to be paid in monthly installments over a 10-year period. Let's first calculate your monthly payment amount.
This type of loan is called an annuity (where you pay off a loan in installments). Here, the principle is $20000 (P), on which you will pay back the lender at an interest rate of 2.57% (i) per year for 10 (n) years, in 12 (q) equal payments per year. The monthly payment M is:
M = Pi/[q(1-[1+(i/q)]-nq)]
Plugging the numbers in we get M = $189.18.
To get the total interest payed over 10 years on this loan, calculate Mnq - P, which is $2701.60.
