Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $7668

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 = $7668 – $5400 = $2268

Thus, Simple Interest = $2268

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 × 2268}/_{5400 × 7}

= ²²⁶⁸⁰⁰/₃₇₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5400

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2268 (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 = 7% of Principal

= 7% of $5400

= ⁷/₁₀₀ × 5400

= ^{7 × 5400}/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 $2268, then the time = ¹/₃₇₈ × 2268 years

= ^{1 × 2268}/₃₇₈ years

= ²²⁶⁸/₃₇₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?

(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?

(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(5) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?

(6) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) If Joshua paid $5292 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.

(9) What amount does David have to pay after 5 years if he takes a loan of $3400 at 3% simple interest?

(10) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.