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 $7200 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7200

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 = $7200 – $4500 = $2700

Thus, Simple Interest = $2700

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 × 2700}/_{4500 × 10}

= ²⁷⁰⁰⁰⁰/₄₅₀₀₀

= 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) = $4500

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

Simple Interest = $2700 (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 $2700, then the time = ¹/₄₅₀ × 2700 years

= ^{1 × 2700}/₄₅₀ years

= ²⁷⁰⁰/₄₅₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.

(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.

(6) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.

(7) Andrew had to pay $5520 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?

(9) How much loan did Brian borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8280 to clear it?

(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.