Learning present value calculation formula:
An annuity is a series of payments of a fixed amount of money at regular intervals of time.usually the interval is a year. But the interval may be half year, quarter year or monthly, etc., unless otherwise stated about this interval, it will be taken as a year. The payments may be for a fixed number of years or to continue forever. If it is for a fixed number of years then the annuity is called Annuity certain. If it is continued forever it is called perpetual Annuity, or perpetuity.
If each payment of an annuity is made at the end of each period the annuity is called Immediate annuity. If each payment is made at the beginning of each period, the annuity is called annuity due.
When an annuity is payable after a lapse of a given period, it is called as Deferred Annuity.
Present Value Definition and Calculation Formula:
The present value of an annuity is the sum of all present values of various instalments of the annuity.
Let us learn the present value calculation formula for different annuities.
Present value of an immediate annuity = `(a)/(i)[ 1 - (1+i)^(-n)]` where $a is the present value to be paid at the end of first year at the rate of i per dollar.
Note 1:
If the annuity is the annuity due, then
P = `(a(1+i))/(i)[1- 1/(1+i)^n]`
Note 2:
In case of immediate annuity if the instalments are paid k times a year, then
P = `(a)/(i)[ 1 - 1/(1+i/k)^nk]`
Present value of deferred annuity is `(a)/(1+i)^d.1/i[1-(1+i)^-n]`
Present value of perpetuity deferred for d years = `(1)/(1+i)^d xx 1/i`
Understanding Difference Quotient Formula is always challenging for me but thanks to all math help websites to help me out.
Problems Using Present Value Calculation Formula
Find the present value of an annuity of $5000 per annum for 12 years, the interest being 4% per annum compounded annually.
a = $5000, n = 12 years, i = 0.04
P = `(a)/(i)[ 1 - 1/(1+i)^n]`
Substituting the values we get, P = $46925
A man retires at the age of 60 and earns a pension of $8700 a year. He wants to commute one third of his pension. Find the amount he will receive, if the expectations of life at this age be 10 years, and the interest is compounded at 4% per annum.
Solution:
Annual pension = $8700
Commuted amount = 1/3 of the pension
So, a = 2900
n = 10 years
i = 0.04
Substituting the values in the formula we get P = $23519
An annuity is a series of payments of a fixed amount of money at regular intervals of time.usually the interval is a year. But the interval may be half year, quarter year or monthly, etc., unless otherwise stated about this interval, it will be taken as a year. The payments may be for a fixed number of years or to continue forever. If it is for a fixed number of years then the annuity is called Annuity certain. If it is continued forever it is called perpetual Annuity, or perpetuity.
If each payment of an annuity is made at the end of each period the annuity is called Immediate annuity. If each payment is made at the beginning of each period, the annuity is called annuity due.
When an annuity is payable after a lapse of a given period, it is called as Deferred Annuity.
Present Value Definition and Calculation Formula:
The present value of an annuity is the sum of all present values of various instalments of the annuity.
Let us learn the present value calculation formula for different annuities.
Present value of an immediate annuity = `(a)/(i)[ 1 - (1+i)^(-n)]` where $a is the present value to be paid at the end of first year at the rate of i per dollar.
Note 1:
If the annuity is the annuity due, then
P = `(a(1+i))/(i)[1- 1/(1+i)^n]`
Note 2:
In case of immediate annuity if the instalments are paid k times a year, then
P = `(a)/(i)[ 1 - 1/(1+i/k)^nk]`
Present value of deferred annuity is `(a)/(1+i)^d.1/i[1-(1+i)^-n]`
Present value of perpetuity deferred for d years = `(1)/(1+i)^d xx 1/i`
Understanding Difference Quotient Formula is always challenging for me but thanks to all math help websites to help me out.
Problems Using Present Value Calculation Formula
Find the present value of an annuity of $5000 per annum for 12 years, the interest being 4% per annum compounded annually.
a = $5000, n = 12 years, i = 0.04
P = `(a)/(i)[ 1 - 1/(1+i)^n]`
Substituting the values we get, P = $46925
A man retires at the age of 60 and earns a pension of $8700 a year. He wants to commute one third of his pension. Find the amount he will receive, if the expectations of life at this age be 10 years, and the interest is compounded at 4% per annum.
Solution:
Annual pension = $8700
Commuted amount = 1/3 of the pension
So, a = 2900
n = 10 years
i = 0.04
Substituting the values in the formula we get P = $23519
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