Question - Compound Interest Calculation for Fixed Deposit Account
Solution:
The formula to calculate the compound interest for a fixed deposit is \( A = P(1 + \frac{r}{n})^{nt} \), where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested or borrowed for, in years.
Given that the interest is compounded annually (\( n = 1 \)), the interest rate is 6% (\( r = 0.06 \)), the time \( t \) is 1.5 years (18 months) and the future amount (\( A \)) is RM 1,710.
We must now solve for \( P \) using the given values.
\[
A = P(1 + r)^t
\]
Substitute the given values:
\[
1,710 = P(1 + 0.06)^{1.5}
\]
\[
1,710 = P(1.06)^{1.5}
\]
Now, solve for \( P \):
\[
P = \frac{1,710}{(1.06)^{1.5}}
\]
\[
P \approx \frac{1,710}{1.093443}
\]
\[
P \approx 1564.769
\]
So, the principal amount \( P \) is approximately RM 1,564.77.
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