Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9350 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $9350

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 = $9350 – $5500 = $3850

Thus, Simple Interest = $3850

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 × 3850}/_{5500 × 10}

= ³⁸⁵⁰⁰⁰/₅₅₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = $5500

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $3850 (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 = 10% of Principal

= 10% of $5500

= ¹⁰/₁₀₀ × 5500

= ^{10 × 5500}/₁₀₀

= ⁵⁵⁰⁰⁰/₁₀₀ = 550

Thus, simple Interest for 1 year = $550

Now,

∵ If the simple Interest is $550, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₀ years

∴ If the simple Interest is $3850, then the time = ¹/₅₅₀ × 3850 years

= ^{1 × 3850}/₅₅₀ years

= ³⁸⁵⁰/₅₅₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.

(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(3) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.

(5) 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.

(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?

(7) How much loan did Barbara borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6937.5 to clear it?

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 5% simple interest for 7 years.

(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.

(10) How much loan did Laura borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9812.5 to clear it?