Bill Baxter has 28,000 to invest for a year. You can lend it to a sister who has agreed to pay 8% simple interest for the year. Or you can invest it with the bank at 6% compounded quarterly for the year. How much additional interest with a simple interest loan to sister generate? Finally effective interest rate for both investments.

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windyyork windyyork · Answer 1 · 2019-12-05T06:30:23+01:00

Answer: Additional interest of $521.82 with a simple interest loan to sister generate.

Step-by-step explanation:

Since we have given that

Principal = $28000

Rate of interest at simple interest = 8%

Number of year = 1

so, Interest becomes,

[tex]\dfrac{28000\times 8\times 1}{100}\\\\=280\times 8\\\\=\$2240[/tex]

Rate of interest compounded quarterly = 6%

Amount becomes,

[tex]A=P(1+\dfrac{r}{400})^{4n}\\\\A=28000(1+\dfrac{6}{400})^4\\\\A=28000(\dfrac{406}{400})^4\\\\A=\$29718.18[/tex]

So, Interest would be

[tex]Amount-Principal\\\\=29718.18-28000\\\\=\$1718.18[/tex]

Hence, Additional interest is given by

[tex]2240-1718.18\\\\=\$521.82[/tex]

Hence, Additional interest of $521.82 with a simple interest loan to sister generate.