Respuesta :
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: [tex]A=P(1+rt)[/tex]
where:
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is number of years
- Compound interest formula: [tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
where:
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is he number of years
[tex]n[/tex] 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 [tex]P=1500[/tex], [tex]t=5[/tex], and since the interest is compounded annually (1 time a year), [tex]n=1[/tex]. To find the interest rate in decimal form, we are going to divide it by 100%: [tex]r= \frac{4}{100} =0.04[/tex]. Now that we have all the values lets replace them in our compound interest formula:
[tex]A=1500(1+ \frac{0.04}{1}) ^{(1)(5)} [/tex]
[tex]A=1824.98[/tex]
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 [tex]P=1500[/tex], [tex]t=5[/tex], and [tex]r= \frac{4}{100} =0.04[/tex]. Lets replace those values in our simple interest formula:
[tex]A=1500(1+(0.04)(5))[/tex]
[tex]A=1800[/tex]
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 [tex]1824.98-1800=24.98[/tex]
2.
a. Here we are going to use our compound interest formula. We know that [tex]P=2000[/tex], [tex]t=1[/tex] and [tex]r= \frac{8}{100} =0.08[/tex]. We also know that the interest is compounded Quaternary (4 times per year), so [tex]n=4[/tex]. Now that we have all our values lets replace them into our formula:
[tex]A=2000(1+ \frac{0.08}{4} )^{(4)(1)} [/tex]
[tex]A=2164.86[/tex]
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 [tex]P=2000[/tex], [tex]t=1[/tex], and [tex]r= \frac{8}{100} =0.08[/tex]. Once again, lets replace those values in our formula:
[tex]A=2000(1+(0.08)(1))[/tex]
[tex]A=2160[/tex]
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 [tex]2164.86-2160=4.86[/tex]
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 [tex]P=3200[/tex], [tex]t=3[/tex], and [tex]r= \frac{3.5}{100} =0.035[/tex]. Now we can replace those values into our formula to get:
[tex]A=3200(1+(0.035)(3))[/tex]
[tex]A=3536[/tex]
Now, to find the interest earned for Bank A we are going to subtract [tex]P[/tex] from [tex]A[/tex]
[tex]InterestEarned=3536-3200=336[/tex]
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 [tex]P=3200[/tex], [tex]t=3[/tex], [tex]r= \frac{3.4}{100} =0.034[/tex], and since the interest is compounded annually (1 time a year), [tex]n=1[/tex]. Now that we have all the values, lets replace them in our formula to get:
[tex]A=3200(1+ \frac{0.034}{1} )^{(1)(3)} [/tex]
[tex]A=3537.62[/tex]
Now, to find the interest earned for Bank A we are going to subtract [tex]P[/tex] from [tex]A[/tex]:
[tex]InterestEarned=3537.62-3200=337.62[/tex]
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 [tex]3537.62-3536=1.62[/tex]
- Simple interest formula: [tex]A=P(1+rt)[/tex]
where:
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is number of years
- Compound interest formula: [tex]A=P(1+ \frac{r}{n} )^{nt} [/tex]
where:
[tex]A[/tex] is the final investment value
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is he number of years
[tex]n[/tex] 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 [tex]P=1500[/tex], [tex]t=5[/tex], and since the interest is compounded annually (1 time a year), [tex]n=1[/tex]. To find the interest rate in decimal form, we are going to divide it by 100%: [tex]r= \frac{4}{100} =0.04[/tex]. Now that we have all the values lets replace them in our compound interest formula:
[tex]A=1500(1+ \frac{0.04}{1}) ^{(1)(5)} [/tex]
[tex]A=1824.98[/tex]
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 [tex]P=1500[/tex], [tex]t=5[/tex], and [tex]r= \frac{4}{100} =0.04[/tex]. Lets replace those values in our simple interest formula:
[tex]A=1500(1+(0.04)(5))[/tex]
[tex]A=1800[/tex]
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 [tex]1824.98-1800=24.98[/tex]
2.
a. Here we are going to use our compound interest formula. We know that [tex]P=2000[/tex], [tex]t=1[/tex] and [tex]r= \frac{8}{100} =0.08[/tex]. We also know that the interest is compounded Quaternary (4 times per year), so [tex]n=4[/tex]. Now that we have all our values lets replace them into our formula:
[tex]A=2000(1+ \frac{0.08}{4} )^{(4)(1)} [/tex]
[tex]A=2164.86[/tex]
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 [tex]P=2000[/tex], [tex]t=1[/tex], and [tex]r= \frac{8}{100} =0.08[/tex]. Once again, lets replace those values in our formula:
[tex]A=2000(1+(0.08)(1))[/tex]
[tex]A=2160[/tex]
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 [tex]2164.86-2160=4.86[/tex]
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 [tex]P=3200[/tex], [tex]t=3[/tex], and [tex]r= \frac{3.5}{100} =0.035[/tex]. Now we can replace those values into our formula to get:
[tex]A=3200(1+(0.035)(3))[/tex]
[tex]A=3536[/tex]
Now, to find the interest earned for Bank A we are going to subtract [tex]P[/tex] from [tex]A[/tex]
[tex]InterestEarned=3536-3200=336[/tex]
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 [tex]P=3200[/tex], [tex]t=3[/tex], [tex]r= \frac{3.4}{100} =0.034[/tex], and since the interest is compounded annually (1 time a year), [tex]n=1[/tex]. Now that we have all the values, lets replace them in our formula to get:
[tex]A=3200(1+ \frac{0.034}{1} )^{(1)(3)} [/tex]
[tex]A=3537.62[/tex]
Now, to find the interest earned for Bank A we are going to subtract [tex]P[/tex] from [tex]A[/tex]:
[tex]InterestEarned=3537.62-3200=337.62[/tex]
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 [tex]3537.62-3536=1.62[/tex]
