mcqs Math Simple Interest Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan. 7457

Question: Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.

(A)  5.25
(B)  8.75
(C)  7
(D)  10.5

Correct Answer 7

Solution And Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $9656

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9656 – $6800 = $2856

Thus, Simple Interest = $2856

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2856}/_{6800 × 6}

= ²⁸⁵⁶⁰⁰/₄₀₈₀₀

= 7 years (using formula)

Thus, Time (T) = 7 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $6800

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2856 (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 = 6% of Principal

= 6% of $6800

= ⁶/₁₀₀ × 6800

= ^{6 × 6800}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $2856, then the time = ¹/₄₀₈ × 2856 years

= ^{1 × 2856}/₄₀₈ years

= ²⁸⁵⁶/₄₀₈ = 7 years

Thus, time (T) = 7 years Answer