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almond37 [142]
3 years ago
13

3.

Mathematics
1 answer:
Vitek1552 [10]3 years ago
8 0
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} } ]
where
FV is the future value
P is the periodic deposit 
r is the interest rate in decimal form 
n is the number of times the interest is compounded per year
k is the number of deposits per year

We know for our problem that P=420 and t=15. To convert the interest rate to decimal form, we are going to divide the rate by 100%: r= \frac{10}{100} =0.1. Since Ruben makes the deposits every 6 months, k=2. The interest is compounded semiannually, so 2 times per year; therefore, k=2.
Lets replace the values in our formula:

FV=(1+ \frac{r}{n} )*P[ \frac{(1+ \frac{r}{n})^{kt}-1 }{ \frac{r}{n} } ]
FV=(1+ \frac{0.1}{2} )*420[ \frac{(1+ \frac{0.1}{2})^{(2)(15)}-1 }{ \frac{01}{2} } ]
FV=29299.53

We can conclude that the correct answer is <span>$29,299.53</span>
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