Simple Interest
Math MCQs

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.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6300

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

Amount (A) = $9324

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

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

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $9324 – $6300 = $3024

Thus, Simple Interest = $3024

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

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

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

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

Similar Questions

(1) If James paid $3240 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.

(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?

(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.

(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.

(8) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.

(10) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.