Profit

Number Theory Level 1

Fill in the blank:

Consider a bank that gives a simple interest rate of $i$ %.

If I deposit $6500 into this bank, the money will be accumulated to $8840 after 4 years.
If I deposit $ $\text{\_\_\_\_\_}$ into this bank, the money accumulated will be $10200 after 4 years.

The answer is 7500.

1 solution

Jacob Grays
Apr 15, 2018

The first dot point gives us enough information to determine the interest rate, $R$ :

$SI = \frac{PRT}{100}$

$R =$ $\frac{100SI}{PT}$

Where $SI = 8840 - 6500 = 2340$ ; $P = 6500$ ; and $T = 4$ .

Therefore $R = 9$ , i.e., the interest rate is 9%. We will use this interest rate to find the principal amount that satisfies the scenario in the second dot point. Here we know that the principal plus the simple interest accrued after 4 years is $10200. Mathematically:

$P + SI = 10200 = P + \frac{PRT}{100}$

$10200 = P(1 + \frac{RT}{100})$

$10200 = P(1 + 0.36)$

$P = 7500$

Profit

The answer is 7500.

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