Simple Interest
Math MCQs

Question :    Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $6930 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) = 9% per annum

Amount (A) = $6930

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 = $6930 – $4500 = $2430

Thus, Simple Interest = $2430

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 × 2430}/_{4500 × 9}

= ²⁴³⁰⁰⁰/₄₀₅₀₀

= 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) = 9% per annum

Simple Interest = $2430 (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 $4500

= ⁹/₁₀₀ × 4500

= ^{9 × 4500}/₁₀₀

= ⁴⁰⁵⁰⁰/₁₀₀ = 405

Thus, simple Interest for 1 year = $405

Now,

∵ If the simple Interest is $405, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₅ years

∴ If the simple Interest is $2430, then the time = ¹/₄₀₅ × 2430 years

= ^{1 × 2430}/₄₀₅ years

= ²⁴³⁰/₄₀₅ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

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

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?

(3) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(4) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 4 years.

(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.

(6) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?