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 $12600 to clear the loan, then find the time period of the loan. 7986

Question: Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 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) = $7000

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

Amount (A) = $12600

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $12600 – $7000 = $5600

Thus, Simple Interest = $5600

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5600}/_{7000 × 8}

= ⁵⁶⁰⁰⁰⁰/₅₆₀₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $7000

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

Simple Interest = $5600 (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 $5600, then the time = ¹/₅₆₀ × 5600 years

= ^{1 × 5600}/₅₆₀ years

= ⁵⁶⁰⁰/₅₆₀ = 10 years

Thus, time (T) = 10 years Answer