Question

You are considering an annuity which costs $54700 today. The annuity pays $6100 a year. The rate of return is 7 percent. What is the length of the annuity time period? (Do not round intermediate calculations.)

rev: 07_11_2013_QC_32664, 07_12_2013_QC_32664

14.60 years

16.21 years

24.58 years

5.83 years

7.20 years

Answer 1

The Answer is 7.20 years the solution for the same is as below:
Annuity Cost Today = 54700
Installment payment = 6100
Interest rate is = 7% and Time i.e Duration "t" is to be found out

Formulae for Annuity is as follows
A = m[(1+r/n)^nt-1]/r/n
Where A is Annuity amount i.e 54700
m= monthly installment ( Here we are taking yearly installment instead of Monthly) i.e 6100
r is the rate of Interest i.e 7%
n is the no of payment here we will take 1 as it is yearly payment
t is the time or duration

therefore on substuting values as per above formulae we have the following equation

54700= 6100[(1+0.07)^t-1]/0.07

on further solving we have below situation

54700/6100*0.07=1.07^t-1

on further solving the equation we have the following

0.6277= 1.07^t-1Which is equal to 1.6277 = 1.07^t

Now using log table we can solve the above equation as below

Log 1.6277 = Log 1.07^t which as per log principles is equal to Log 1.6277 = t * Log 1.07

with log values we have following situation

0.21157 = t * 0.02938

t= 0.21157/0.02938

t= 7.20