Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 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.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $9000

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 = $9000 – $4500 = $4500

Thus, Simple Interest = $4500

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 × 4500}/_{4500 × 10}

= ⁴⁵⁰⁰⁰⁰/₄₅₀₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $4500

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

Simple Interest = $4500 (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 $4500

= ¹⁰/₁₀₀ × 4500

= ^{10 × 4500}/₁₀₀

= ⁴⁵⁰⁰⁰/₁₀₀ = 450

Thus, simple Interest for 1 year = $450

Now,

∵ If the simple Interest is $450, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₅₀ years

∴ If the simple Interest is $4500, then the time = ¹/₄₅₀ × 4500 years

= ^{1 × 4500}/₄₅₀ years

= ⁴⁵⁰⁰/₄₅₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6120 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(4) How much loan did Donna borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8562.5 to clear it?

(5) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(6) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?

(7) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 3 years.

(8) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?

(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.