mcqs Math Simple Interest Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan. 7607

Question: Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9324 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) = $6300

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

Amount (A) = $9324

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9324 – $6300 = $3024

Thus, Simple Interest = $3024

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3024}/_{6300 × 6}

= ³⁰²⁴⁰⁰/₃₇₈₀₀

= 8 years (using formula)

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

Here, we have

Principal (P) = $6300

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

Simple Interest = $3024 (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 $6300

= ⁶/₁₀₀ × 6300

= ^{6 × 6300}/₁₀₀

= ³⁷⁸⁰⁰/₁₀₀ = 378

Thus, simple Interest for 1 year = $378

Now,

∵ If the simple Interest is $378, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₈ years

∴ If the simple Interest is $3024, then the time = ¹/₃₇₈ × 3024 years

= ^{1 × 3024}/₃₇₈ years

= ³⁰²⁴/₃₇₈ = 8 years

Thus, time (T) = 8 years Answer