Manuals/calci/IPMT

IPMT(r,pr,np,pv,fv,type)

• $r$ is the annual rate of interest.
• $pr$ is the period of to find the interest rate.
• $np$ is the number of installments.
• $pv$ is the present value.
• $fv$ is the future value.
• $type$ is either 1 or 0.

Description

• This function gives amount of interest for a particular time, according to the periodic, fixed payments and fixed interest rate.
• This function can be used to calculate the payments for a loan or the future value of an investment.
• In $IPMT(r,pr,np,pv,fv,type)$, where $r$ is the rate of interest for a year
• $pr$ is the period for which the interest payment is to be calculated. It must be a value between $1$ and $np$.
• $np$ is the total number of periods over which the loan or investment is to be paid.
• $pv$ is the present value of the loan.
• $fv$ is the future value of the loan, at the end of $np$ payment.
• $type$ is the number $0$ or $1$.
• When type value is $0$ means the payment is made at the end of the period and type value is $1$ means the payment is made at the beginning of the period
• Here the arguments $fv$ and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle type} are optional.
• Suppose we omit the value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle fv} , then it will consider the value as Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} .
• Also when we are not giving the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle type} value, the default value is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} .
• Suppose we calculate the monthly payments instead of annual payment, for the argument Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} we have to divide by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 12} and the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle np} value we have multiply with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 12} .
• For e.g. The monthly payments on a 5 year loan at 10% annual interest, we have to give the arguments Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle np} as 10%/12 for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} and 5*12 for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle np} .
• This function will give result as error when

Any one of the argument is non-numeric
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle pr < 0}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle pr > np}

Examples

• Calculate the interest payment during half yearly 1 and 2 of a loan for 50,000, that is to be reduced to 10,000 over a period of 3 years, by a series of constant half-yearly payments.
• Interest is charged at a rate of 4.5% per year and the payment is made at the beginning of each half year.
• IPMT(4.5%/2,3,2*2,50000,10000,1)=-454.78 (EXCEL)=-480.666(CALCI)

2.The interest payment for a $55000 investment that earns 7.50% annually for 15 years.

• The interest payment is calculated for the 5th year and payments are due at the end of each year.

IPMT(7.5%/1, 5, 15*1, 55000)=-3418.570

References

Binary Logarithm