You wrote
C.I. = 7,500[.02] = 150
C.I. = 7650 [.02] = 153
In particular you used [.02] there. The problem stated however "4% per annum", so you should have used [.04] instead.
7500[.04] = 300
7800[.04] = 312
300+312 = 612
Your answer and method would have been correct if the problem read "Find compound interest on 7500 dollars at 2% per annum for 2 years, compounded annually." or if it read as "Find compound interest on 7500 dollars at 4% per annum for 1 year, compounded semi-annually."
Edit: In response to your question on how to interpret the answer key's solution.
[7500[1 + 4/100]2], although poorly typed is meant to be $7500\cdot[1+\frac{4}{100}]^2$
Interest rate formula: $$F = P[1+\frac{r}{n}]^{ny}$$ where $F$ = future value, $P$ = initial value [principle], $r$ = APR [interest rate per year], $n$ = number of times per year it is compounded, $y$ = number of years.
In this case, $P=7500$, $r=.04$, $n=1$, and $y=2$, and $F$ is unknown. So, by the formula above, $F=7500[1+.04]^2$. With a bit of arithmetical simplifications, $=7500[1.04]^2 = 7500[\frac{26}{25}\cdot\frac{26}{25}]$
Often times you will see the formula rewritten as $F = P[1+i]^t$ where $i$= interest rate per payment period = $\frac{r}{n}$, and $t$ = number of payment periods = $n\cdot y$.
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Important Civilization in Rajasthan
15 Questions 15 Marks 10 Mins
Given:
Principal [P] = Rs. 7500
Rate % [R]= 4% per annum
Time Period [T] = 2 years
Formula Used:
\[{\rm{Amount}} = {\rm{P}}{\left[ {1 + \;\frac{R}{{100}}} \right]^T}\;\]
Calculation:
\[{\rm{Amount}} = 7500{\left[ {1 + \;\frac{4}{{100}}} \right]^2}\;\]
⇒ Amount = 7500 × [104/100]2
⇒ [7500 × 26 × 26]/[25 × 25]
⇒ 12 × 676 = Rs. 8112
∴ The Amount After 2 years will be Rs. 8112
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Solution
The correct option is C
Rs.612
Using the formula A = P[1+r100]n and substituting P = ₹ 7500 , t = 2 years , r = 4 p.a , we have
A = ₹7500× [1+ 4100]2 =₹7500× 2625× 2625= ₹8112.
C.I = A - P
∴
C.I.=
₹8112−7500
=₹612.
Solve
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