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Yvette is considering taking out a loan with a principal of $16,200 from one of two banks. Bank F charges an interest rate of 5. 7%, compounded monthly, and requires that the loan be paid off in eight years. Bank G charges an interest rate of 6. 2%, compounded monthly, and requires that the loan be paid off in seven years. How would you recommend that Yvette choose her loan?.

Sagot :

Marvineetesh3idn

A loan is the amount of money that a borrower borrows for a specific purpose and for a limited period of time. A bank loan from bank G is more favorable than bank A.

What is a loan?

A loan is the amount of money that is taken by the borrower from the banks or other financial institutions for a particular purpose. Here the lender of money charger some more amount as interest for the use of the money lent.

Computation of interest:

For bank F:

Principal(P) = $16,200

Interest rate (r) = 5.7%  

Compounded Monthly:

[tex]\dfrac{\frac{5.7}{12} }{100}=0.0047[/tex]

Time Period(t) = 8 years

Now, apply the formula of present value(PV), we have

[tex]\text{PV}= \text{A}\dfrac{(1+i)^n-1}{i\times(1+i)^n}\\\\\\\$16,200=\text{A}\dfrac{(1+0.0047)^9^6-1}{0.0047\times(1+0.0047)^9^6}\\\\\\\\\text{A} = \$ 210.53[/tex]

Then,

The total amount to be paid on the loan is:

[tex]= \$210.53\times8\times12 = \$20,210.53[/tex]

Interest to be paid on loan:

[tex]\text{Interest}=\text{Amount}\text{Principal}\\\\\\\text{Interest}= \$20,210.53-\$16,200\\\\\\\text{Interest}=\$4,010.53[/tex]

For bank G:

Interest Rater(r)=6.2%,

Compounded Monthly:

[tex]\dfrac{\frac{6.2}{12} }{100} = 0.00516[/tex]

Time(t)= 7 years

Here also, apply the formula of present value(PV) and put the values in the formula:

[tex]\text{PV}= \text{A}\dfrac{(1+i)^n-1}{i\times(1+i)^n}\\\\\\\$16,200=\text{A}\dfrac{(1+0.0051)^8^4-1}{0.0051\times(1+0.0051)^8^4}\\\\\\\\\text{A} = \$ 238.21[/tex]

The total amount to be paid on the loan is:

[tex]\$238.01\times7\times12 = \$20,010.05[/tex]

Interest to be paid on loan:

[tex]\text{Interest}=\text{Amount}\text{Principal}\\\\\\\text{Interest}= \$20,010.05-\$16,200\\\\\\ \text{Interest}= \$3,810.05[/tex]

The amount of interest in Bank G is less than the amount of interest in bank F.

Therefore, bank G is favorable to Yvette.

Learn more about the loan, refer to:

https://brainly.com/question/11794123

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