mcqs Math Simple Interest David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan. 7902

Question: David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(A)  7.5
(B)  12.5
(C)  10
(D)  15

Correct Answer 10

Solution And Explanation

Solution

Given,

Principal (P) = $4800

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

Amount (A) = $7680

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $7680 – $4800 = $2880

Thus, Simple Interest = $2880

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2880}/_{4800 × 6}

= ²⁸⁸⁰⁰⁰/₂₈₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 years (from time taken before calculation)Answer

Here, we have

Principal (P) = $4800

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

Simple Interest = $2880 (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 $4800

= ⁶/₁₀₀ × 4800

= ^{6 × 4800}/₁₀₀

= ²⁸⁸⁰⁰/₁₀₀ = 288

Thus, simple Interest for 1 year = $288

Now,

∵ If the simple Interest is $288, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₈ years

∴ If the simple Interest is $2880, then the time = ¹/₂₈₈ × 2880 years

= ^{1 × 2880}/₂₈₈ years

= ²⁸⁸⁰/₂₈₈ = 10 years

Thus, time (T) = 10 years Answer