Question

in the following ordinary annuity interest is compounded with each payment and the payment is made at the end of the compounding period. find the accumulated amount of the annuity. 4,500 annually at 6% for 10 years

Answer 1

Answer: $59313.58

Step-by-step explanation:

We know that formula we use to find the accumulated amount of the annuity ( ordinary annuity interest is compounded ) is given by :-

$FV=A(\frac{(1+\frac{r}{m})^{mt})-1}{\frac{r}{m}})$, where A is the annuity payment deposit, r is annual interest rate , t is time in years and n is number of periods.

Given : Annuity payment deposit :A= $4500

rate of interest :r= 6%=0.06

No. of periods : m= 1   [∵ its annual]

Time : t= 10 years

Now we get,

$FV=(4500)(\frac{(1+\frac{0.06}{1})^{1\times10})-1}{\frac{0.06}{1}})\\\\\Rightarrow\ FV=(4500)(\frac{(1.06)^{10})-1}{0.06})\\\\\Rightarrow\ FV=(4500)(\frac{0.79084769654}{0.06})\\\\\Rightarrow\ FV=(4500)(13.1807949423)\\\\\Rightarrow\ FV=59313.5772407\approx59313.58$

∴ the accumulated amount of the annuity= $59313.58