Respuesta :
In order for you to be able to determine on which is the best effective interest rate, we need to compute each interest and see on how much would it accrue after it matures. The formula to use is the compound interest formula which is A=P(1+r/n)^nt, wherein A is the amount of due including the interest, P as the principal, r as the interest rate, n as the number of times it would be compounded per year and t as the number of years it would be loaned. To reassign the formula with each given interest rate, and assuming that the amount to be loaned would be 1,000 and the number of years it would be loaned will be 5 years, the amount due after 5 years for the 8.254% compounded daily will be 1,510.82, for the 8.474% compounded weekly will be 1,527.03, for the 8.533% compounded monthly will be 1,529.80, for the 8.604% compounded yearly will be 1,510.88. The best effective interest rate offer would be the 8.254% compounded daily.
Loan L that has a nominal rate of [tex]8.254\%[/tex], compounded daily offer Craig the best effective interest rate.
Further explanation:
Given:
The options are as follows,
(a). Loan L has a nominal rate of [tex]8.254\%[/tex], compounded daily.
(b). Loan M has a nominal rate of [tex]8.474\%[/tex], compounded weekly.
(c). Loan N has a nominal rate of [tex]8.533\%[/tex], compounded monthly.
(d). Loan O has a nominal rate of [tex]8.604\%[/tex], compounded yearly.
Explanation:
The compound interest rate formula can be expressed as follows,
[tex]\boxed{A = P{{\left( {1 + \frac{r}{n}} \right)}^{nt}}}[/tex]
Here, A represents the amount, P represents the principal amount, r represents the interest rate n represents the number of times interest rate compounded and t represents the time.
Consider the amount as [tex]\$100[/tex] for 2 years.
The amount after year if the interest rate is [tex]8.254\%[/tex], compounded daily can be calculated as follows,
[tex]\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08254}}{{365}}} \right)^{2 \times 365}} \\&= \$ 117.95 \\\end{aligned}[/tex]
The amount after year if the interest rate is [tex]8.474\%[/tex], compounded weekly can be calculated as follows,
[tex]\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08474}}{{52}}} \right)^{2 \times 52}}\\&= \$ 118.45 \\\end{aligned}[/tex]
The amount after year if the interest rate is [tex]8.533\%,[/tex] compounded monthly can be calculated as follows,
[tex]\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08533}}{{12}}} \right)^{2 \times 12}}\\&= \$ 118.54\\\end{aligned}[/tex]
The amount after year if the interest rate is [tex]8.254\%[/tex], compounded daily can be calculated as follows,
[tex]\begin{aligned}{\text{A}} &= 100{\left( {1 + \frac{{0.08604}}{1}} \right)^{2 \times 1}} \\&= \$ 117.95\\\end{aligned}[/tex]
Loan L that has a nominal rate of [tex]8.254\%[/tex], compounded daily offer Craig the best effective interest rate.
Option (a) is correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is not correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Simple interest
Keywords: Craig, four loans, loan L, loan M, loan N, loan O, nominal rate, compounded daily, effective rate, compounded monthly, compounded weekly, compounded yearly, interest rate, Principal, invested, interest rate, account, effective interest rate, total interest, amount.
