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MM150 Survey of Mathematics
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Will you earn more interest in one year by depositing $$ 3000$ in a simple interest account that pays $7 %$ or in an account that pays $6.9 %$ interest compounded daily? How much more interest will you earn?
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In which account will you earn more interest? Select the correct choice below and fill in the answer box within your choice.
(Round to the nearest dollar as needed.)
A. You will earn $$$ more interest in the compoundinterest account than in the simpleinterest account.
B. You will earn $$$ more interest in the simpleinterest account than in the compoundinterest account.
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Thus, the compound interest account earns approximately $4.29 more interest than the simple interest account in one year. So, the final answer is $4.29$ .

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Step 1 ：Given that the principal amount (P) is $3000, t h e r a t e o f i n t e r e s t f o r t h e s i m p l e i n t e r e s t a c c o u n t (R) i s 0.07, a n d t h e t i m e (T) i s 1 y e a r, w e c a n c a l c u l a t e t h e s i m p l e i n t e r e s t u s i n g t h e f o r m u l a I = P R T . T h i s g i v e s u s a s i m p l e i n t e r e s t o f$ 210.

Step 2 ：Next, we calculate the compound interest for an account with the same principal amount (P) of $3000, a n a n n u a l i n t e r e s t r a t e (r) o f 0.069, c o m p o u n d e d d a i l y (n = 365), a n d f o r t h e s a m e t i m e p e r i o d (t) o f 1 y e a r . U s i n g t h e f o r m u l a A = P (1 + r / n)^{(} n t), w e f i n d t h a t t h e c o m p o u n d i n t e r e s t i s a p p r o x i m a t e l y$ 214.29.

Step 3 ：By comparing the two amounts, we can see that the compound interest account earns more interest than the simple interest account.

Step 4 ：To find out how much more interest is earned, we subtract the simple interest from the compound interest. This gives us a difference of approximately $4.29.

Step 5 ：Thus, the compound interest account earns approximately $4.29 more interest than the simple interest account in one year. So, the final answer is $4.29$ .

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