mcqs Math Simple Interest Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan. 7627

Question: Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(A)  6
(B)  10
(C)  8
(D)  12

Correct Answer 8

Solution And Explanation

Solution

Given,

Principal (P) = $5200

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8112

Thus, time (T) = ?

Method (1) Using Formula

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $8112 – $5200 = $2912

Thus, Simple Interest = $2912

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2912}/_{5200 × 7}

= ²⁹¹²⁰⁰/₃₆₄₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $5200

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2912 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 7% of Principal

= 7% of $5200

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = 364

Thus, simple Interest for 1 year = $364

Now,

∵ If the simple Interest is $364, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₄ years

∴ If the simple Interest is $2912, then the time = ¹/₃₆₄ × 2912 years

= ^{1 × 2912}/₃₆₄ years

= ²⁹¹²/₃₆₄ = 8 years

Thus, time (T) = 8 years Answer