Question

Assignment: Compound Interest Investigation

Answer 1

To help Tyler better understand how his money will increase in an account that uses simple interest and one that uses compound interest, we are going to use two formulas: a simple interest formula for the accounts that use simple interest, and a compound interest formula for the accounts that use compound interest.
- Simple interest formula: $A=P(1+rt)$
where:
$A$ is the final investment value 
$P$ is the initial investment 
$r$ is the interest rate in decimal form 
$t$ is number of years
- Compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where: 
$A$ is the final investment value 
$P$ is the initial investment 
$r$ is the interest rate in decimal form
$t$ is he number of years 
$n$ is the number of times the interest is compounded per year

1. 
a. This is a compound interest account, so we are going to use our compound interest formula. We now that $P=1500$, $t=5$, and since the interest is compounded annually (1 time a year), $n=1$. To find the interest rate in decimal form, we are going to divide it by 100%: $r= \frac{4}{100} =0.04$. Now that we have all the values lets replace them in our compound interest formula:
$A=1500(1+ \frac{0.04}{1}) ^{(1)(5)}$
$A=1824.98$
We can conclude that after 5 years he will have $1824.98 in this account.
b. Here we will use our simple interest formula. We know that $P=1500$, $t=5$, and $r= \frac{4}{100} =0.04$. Lets replace those values in our simple interest formula:
$A=1500(1+(0.04)(5))$
$A=1800$
We can conclude that after 5 years he will have $1800 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $1824.98-1800=24.98$

2.
a. Here we are going to use our compound interest formula. We know that $P=2000$, $t=1$ and $r= \frac{8}{100} =0.08$. We also know that the interest is compounded Quaternary (4 times per year), so $n=4$. Now that we have all our values lets replace them into our formula:
$A=2000(1+ \frac{0.08}{4} )^{(4)(1)}$
$A=2164.86$
We can conclude that after 1 year he will have $2164.86 in this account.
b. Here we are going to use our simple interest formula. We know that $P=2000$, $t=1$, and $r= \frac{8}{100} =0.08$. Once again, lets replace those values in our formula:
$A=2000(1+(0.08)(1))$
$A=2160$
We can conclude that after 1 year he will have $2160 in this account.
c. The compound interest account from point a will yield more money than the simple account one from point b. The difference between the tow amounts is $2164.86-2160=4.86$

3.
a. Since Bank A offers an account with a simple interest, we are going to use our simple interest formula. From the question we know that $P=3200$, $t=3$, and $r= \frac{3.5}{100} =0.035$. Now we can replace those values into our formula to get:
$A=3200(1+(0.035)(3))$
$A=3536$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$
$InterestEarned=3536-3200=336$
We can conclude that the interest earned for Bank A is $336
b. Since Bank B offers an account with a compound interest, we are going to use our compound interest formula. We know that $P=3200$, $t=3$, $r= \frac{3.4}{100} =0.034$, and since the interest is compounded annually (1 time a year), $n=1$. Now that we have all the values, lets replace them in our formula to get:
$A=3200(1+ \frac{0.034}{1} )^{(1)(3)}$
$A=3537.62$
Now, to find the interest earned for Bank A we are going to subtract $P$ from $A$:
$InterestEarned=3537.62-3200=337.62$
We can conclude that the interest earned for Bank B is $337.62
c. Even tough the interest returns between the tow Banks are very similar, Bank B offers a slightly better interest over a period of time, which can make a big difference in the long run. If Tyler wants the earn more money, he definitively should deposit his money in Bank B.
d. The compound interest account from Bank B will yield more money than the simple account one from Bank A The difference between the tow amounts is $3537.62-3536=1.62$