At simple interest a man made a deposit of some... - JAMB Mathematics 2023 Question
At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?
15 years
25 years
20 years
30 years
Let's denote the initial deposit as \(P\) and the interest rate as \(r\).
After 10 years at simple interest, the amount in the bank account is three times the initial deposit:
\[ A_{10} = P + 10Pr = 3P \]
Now, we can solve for \(r\):
\[ P + 10Pr = 3P \]
\[ 10Pr = 2P \]
\[ r = \frac{2}{10} = 0.2 \]
Now, we want to find out after how many years the amount will be five times the initial deposit:
\[ A_t = P + tPr = 5P \]
Substitute the known values:
\[ P + t(0.2)P = 5P \]
\[ 1 + 0.2t = 5 \]
\[ 0.2t = 4 \]
\[ t = \frac{4}{0.2} \]
\[ t = 20 \]
Therefore, after 20 years, the amount in the bank account will be five times the initial deposit.
So, the correct answer is 20 years
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