Question

Given annuity of 100 amounts to 3137.12 at 4.5%pa ci.the number of years will be

Answer 1

Answer:

Step-by-step explanation:

Using the formula =A/i{(1+i)^n-1}

3137.12=100/4.5%{(1+4.5%)^n-1}

or,3137.12 X 4.5%/100=(1+4.5%)^n-1

or,1.411704=(1+4.5%)^n-1

or,1.411704+1=(1+45/1000)^n

or,2.411704=(1.045)^n

Now ,multiply 1.045 with itself n no. Of time until u get 2.411704

or,(1.045)^20=(1.045)^n

or,20=n (ANS....)

HOPE THIS IS HELPFULL ........

Answer 2

Answer:

It will take approximately 20 years.

Step-by-step explanation:

Consider the provided information.

It is given that annuity of 100 amounts to 3137.12 at 4.5%pa.

Use the formula of future value.

$F.V=A\times [\frac{(1+r)^n-1}{r}]$

It is given that F.V = 3137.12, A = 100 and r = 4.5% or 0.045

Substitute the respective values in the above formula.

$3137.12=100\times [\frac{(1+0.045)^n-1}{0.045}]$

$\frac{3137.12}{100}=[\frac{(1.045)^n-1}{0.045}]$

$31.3712=\frac{(1.045)^n-1}{0.045}$

$1.411704=(1.045)^n-1$

$2.411704=(1.045)^n$

Taking log both side.

$\:n\ln \left(1.045\right)=\ln \left(2.411704\right)$

$n=\frac{\ln \left(2.411704\right)}{\ln \left(1.045\right)}$

$n=19.99990$

Hence, it will take approximately 20 years.