Respuesta :
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The account which is earning compount interest will earn $41.19 more on interest.
What is simple interest?
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
[tex]\text{Simple Interest}= \dfrac{P \times R \times T}{100}[/tex]
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The interest on account S which earns simple interest at rate of 4.5% can be written as,
[tex]\text{Interest in Account S}= \dfrac{P \times R \times T}{100} = \dfrac{\$400 \times 4.5 \times 10}{100} = $180[/tex]
The interest on accout C which earns compound interest at a rate of 4.5% can be written as,
[tex]\text{Interest in Account C}=P(1+r\%)^n - P\\[/tex]
[tex]\text{Interest in Account C}=\$400(1+4.5\%)^{10} - $400 = $221.19[/tex]
The difference in the amount earned by the two account will be,
[tex]\rm Difference = (Interest\ in\ Account\ C) -(Interest\ in\ Account\ S)[/tex]
[tex]=\$221.19 - \$180\\\\=\$ 41.19[/tex]
Hence, the account which is earning compount interest will earn $41.19 more on interest.
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