If a sum double itself in 8 years, then in how many years it will becomes four times, assuming that the simple interest is calculated.
(A) 16 years
(B) 12 years
(C) 24 years
(D) 20 years

Question

Accepted Answer

> [!TLDR]
> SI to double = 8 years means rate $	imes 8 = 1$; to make it 4 times the interest must be $3P$, requiring $t=24$ years.

### Step 1 — condition for doubling

Doubling means the interest earned equals the principal $P$. With $SI=P\cdot r\cdot t$:

$$P=P\cdot r\cdot 8\ \Rightarrow\ 8r=1\ \Rightarrow\ r=	frac{1}{8}.$$

### Step 2 — condition for becoming four times

Four times the sum means total $=4P$, so interest $=4P-P=3P$:

$$3P=P\cdot r\cdot t\ \Rightarrow\ 3=r\,t=\frac{t}{8}.$$

### Step 3 — solve for $t$

$$t=3	imes 8=24	ext{ years}.$$

Under simple interest the multiple grows linearly, so 4× takes $3	imes$ the doubling time. …

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Step 1 — condition for doubling

Step 2 — condition for becoming four times

Step 3 — solve for $t$

Step 1 — condition for doubling

Step 2 — condition for becoming four times

Step 3 — solve for ttt

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Step 3 — solve for $t$

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