mcqs Math Simple Interest Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 to clear the loan, then find the time period of the loan. 7672

Question: Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10824 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) = $6600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10824

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10824 – $6600 = $4224

Thus, Simple Interest = $4224

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4224}/_{6600 × 8}

= ⁴²²⁴⁰⁰/₅₂₈₀₀

= 8 years (using formula)

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

Here, we have

Principal (P) = $6600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $4224 (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 = 8% of Principal

= 8% of $6600

= ⁸/₁₀₀ × 6600

= ^{8 × 6600}/₁₀₀

= ⁵²⁸⁰⁰/₁₀₀ = 528

Thus, simple Interest for 1 year = $528

Now,

∵ If the simple Interest is $528, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₈ years

∴ If the simple Interest is $4224, then the time = ¹/₅₂₈ × 4224 years

= ^{1 × 4224}/₅₂₈ years

= ⁴²²⁴/₅₂₈ = 8 years

Thus, time (T) = 8 years Answer