mcqs Math Simple Interest Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan. 8010

Question: Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 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) = $6300

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $11970

Thus, time (T) = ?

Method (1) Using Formula

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $11970 – $6300 = $5670

Thus, Simple Interest = $5670

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

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 5670}/_{6300 × 9}

= ⁵⁶⁷⁰⁰⁰/₅₆₇₀₀

= 10 years (using formula)

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

Here, we have

Principal (P) = $6300

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $5670 (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 = 9% of Principal

= 9% of $6300

= ⁹/₁₀₀ × 6300

= ^{9 × 6300}/₁₀₀

= ⁵⁶⁷⁰⁰/₁₀₀ = 567

Thus, simple Interest for 1 year = $567

Now,

∵ If the simple Interest is $567, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₇ years

∴ If the simple Interest is $5670, then the time = ¹/₅₆₇ × 5670 years

= ^{1 × 5670}/₅₆₇ years

= ⁵⁶⁷⁰/₅₆₇ = 10 years

Thus, time (T) = 10 years Answer