What is the value of the logarithm below? (Round your answer to two decimal
1 answer:
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To solve this we are going to use the future value of annuity due formula: ![FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n} )^{kt} -1}{ \frac{r}{n} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%2AP%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7Br%7D%7Bn%7D%20%29%5E%7Bkt%7D%20-1%7D%7B%20%5Cfrac%7Br%7D%7Bn%7D%20%7D%20%5D)
where
is the future value 
is the periodic payment 
is the interest rate in decimal form 
is the number of times the interest is compounded per year 
is the number of payments per year 
is the number of years
We know for our problem that
and 
. To convert the interest rate to decimal for, we are going to divide the rate by 100%:
Since the payment is made quarterly, it is made 4 times per year; therefore,
.
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so
.
Lets replace those values in our formula:
![FV=(1+ \frac{0.1}{4} )*295[ \frac{(1+ \frac{0.1}{4} )^{(4)(6)} -1}{ \frac{0.1}{4} } ]](https://tex.z-dn.net/?f=FV%3D%281%2B%20%5Cfrac%7B0.1%7D%7B4%7D%20%29%2A295%5B%20%5Cfrac%7B%281%2B%20%5Cfrac%7B0.1%7D%7B4%7D%20%29%5E%7B%284%29%286%29%7D%20-1%7D%7B%20%5Cfrac%7B0.1%7D%7B4%7D%20%7D%20%20%5D%20)
We can conclude that the amount of the annuity after 10 years is $9,781.54
where
We know for our problem that
Since the payment is made quarterly, it is made 4 times per year; therefore,
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so
Lets replace those values in our formula:
We can conclude that the amount of the annuity after 10 years is $9,781.54