mcqs Math Simple Interest Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan. 7730

Question: Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11160 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) = $6200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11160

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11160 – $6200 = $4960

Thus, Simple Interest = $4960

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4960}/_{6200 × 10}

= ⁴⁹⁶⁰⁰⁰/₆₂₀₀₀

= 8 years (using formula)

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

Here, we have

Principal (P) = $6200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4960 (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 = 10% of Principal

= 10% of $6200

= ¹⁰/₁₀₀ × 6200

= ^{10 × 6200}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀ = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₀ years

∴ If the simple Interest is $4960, then the time = ¹/₆₂₀ × 4960 years

= ^{1 × 4960}/₆₂₀ years

= ⁴⁹⁶⁰/₆₂₀ = 8 years

Thus, time (T) = 8 years Answer