A man wishes to keep his money in a savings deposit at 25% compound interest so that after three years he can buy a car for N150,000. How much does he need to deposit?
The correct answer is D. N76,800.00
To find out how much the man needs to deposit in order to have N150,000 after three years at a compound interest rate of 25%, we can use the compound interest formula:
\[A = P \left(1 + \frac{r}{100}\right)^n\]
Where:
- \(A\) is the final amount (N150,000)
- \(P\) is the initial principal (amount deposited)
- \(r\) is the annual interest rate (25%)
- \(n\) is the number of compounding periods (3 years)
We need to solve for \(P\):
\[N150,000 = P \left(1 + \frac{25}{100}\right)^3\]
Simplify the fraction:
\[N150,000 = P \left(1 + 0.25\right)^3\]
Calculate the expression inside the parentheses:
\[N150,000 = P \cdot 1.25^3\]
\[N150,000 = P \cdot 1.953125\]
Now, solve for \(P\):
\[P = \frac{N150,000}{1.953125}\]
\[P \approx N76,800.00\]
So, the man needs to deposit approximately N76,800.00.
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