mcqs Math Simple Interest Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan. 7676

Question: Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 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) = $7000

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

Amount (A) = $11480

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11480 – $7000 = $4480

Thus, Simple Interest = $4480

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 4480}/_{7000 × 8}

= ⁴⁴⁸⁰⁰⁰/₅₆₀₀₀

= 8 years (using formula)

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

Here, we have

Principal (P) = $7000

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

Simple Interest = $4480 (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 $7000

= ⁸/₁₀₀ × 7000

= ^{8 × 7000}/₁₀₀

= ⁵⁶⁰⁰⁰/₁₀₀ = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₀ years

∴ If the simple Interest is $4480, then the time = ¹/₅₆₀ × 4480 years

= ^{1 × 4480}/₅₆₀ years

= ⁴⁴⁸⁰/₅₆₀ = 8 years

Thus, time (T) = 8 years Answer