Simple Interest
Math MCQs

Question :    Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5300

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

Amount (A) = $8162

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 = $8162 – $5300 = $2862

Thus, Simple Interest = $2862

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 × 2862}/_{5300 × 9}

= ²⁸⁶²⁰⁰/₄₇₇₀₀

= 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) = $5300

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

Simple Interest = $2862 (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 $5300

= ⁹/₁₀₀ × 5300

= ^{9 × 5300}/₁₀₀

= ⁴⁷⁷⁰⁰/₁₀₀ = 477

Thus, simple Interest for 1 year = $477

Now,

∵ If the simple Interest is $477, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₇₇ years

∴ If the simple Interest is $2862, then the time = ¹/₄₇₇ × 2862 years

= ^{1 × 2862}/₄₇₇ years

= ²⁸⁶²/₄₇₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.

(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.

(6) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.

(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.

(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.