Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $9774

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 = $9774 – $5400 = $4374

Thus, Simple Interest = $4374

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 × 4374}/_{5400 × 9}

= ⁴³⁷⁴⁰⁰/₄₈₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 9% per annum

Simple Interest = $4374 (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 $5400

= ⁹/₁₀₀ × 5400

= ^{9 × 5400}/₁₀₀

= ⁴⁸⁶⁰⁰/₁₀₀ = 486

Thus, simple Interest for 1 year = $486

Now,

∵ If the simple Interest is $486, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₆ years

∴ If the simple Interest is $4374, then the time = ¹/₄₈₆ × 4374 years

= ^{1 × 4374}/₄₈₆ years

= ⁴³⁷⁴/₄₈₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?

(3) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.

(5) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(6) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(7) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(8) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.

(9) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.

(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?