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 $9804 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $9804

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 = $9804 – $5700 = $4104

Thus, Simple Interest = $4104

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 × 4104}/_{5700 × 9}

= ⁴¹⁰⁴⁰⁰/₅₁₃₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $4104 (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 $4104, then the time = ¹/₅₁₃ × 4104 years

= ^{1 × 4104}/₅₁₃ years

= ⁴¹⁰⁴/₅₁₃ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.

(2) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 7 years.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.

(5) Find the amount to be paid if David borrowed a sum of $5400 at 9% simple interest for 8 years.

(6) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.

(7) What amount does James have to pay after 5 years if he takes a loan of $3000 at 3% simple interest?

(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.

(9) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

(10) How much loan did Sandra borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8062.5 to clear it?