Question

If the price today for a security is $3,500 that guarantees you $750 a year, if the opportunity cost of this investment is 4.3%, how long will you receive these payments?

Answer 1

Here $3500 is present value of annuity, Annuity = A = 750$ , r=rate of interest = 4.3% n =?

PV(annuity) = A[1-(1/(1+r)^n /r]

3500 = 750[1-(1/(1+0.043)^n / 0.043]

4.6667 =[1-(1/1.043)^n / 0.043]

4.6667 x 0.043 = 1-(1/1.043)^n

0.2007 = 1 - (1/1.043)^n

(1/1.043)^n = 0.7993

Now let us assume n = 6

(1/1.043)^6 = 0.7768

now let us assume n = 5

(1/1.043)^5 = 0.8102

Thus using interpolation we can find n

n	(1/1.043)^n
6	0.7768
5	0.8102
1 down	0.0334
?	0.0225

=0.0225/0.0334

=0.6737

Thus N = 6-0.6737 = 5.33 Years