Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $8778

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 = $8778 – $5700 = $3078

Thus, Simple Interest = $3078

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 × 3078}/_{5700 × 9}

= ³⁰⁷⁸⁰⁰/₅₁₃₀₀

= 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) = $5700

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

Simple Interest = $3078 (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 $5700

= ⁹/₁₀₀ × 5700

= ^{9 × 5700}/₁₀₀

= ⁵¹³⁰⁰/₁₀₀ = 513

Thus, simple Interest for 1 year = $513

Now,

∵ If the simple Interest is $513, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₃ years

∴ If the simple Interest is $3078, then the time = ¹/₅₁₃ × 3078 years

= ^{1 × 3078}/₅₁₃ years

= ³⁰⁷⁸/₅₁₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 5% simple interest?

(2) 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?

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(4) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(6) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(7) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?

(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 7 years.

(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?

(10) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.