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 $7740 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4500

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

Amount (A) = $7740

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 = $7740 – $4500 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{4500 × 9}

= ³²⁴⁰⁰⁰/₄₀₅₀₀

= 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) = $4500

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

Simple Interest = $3240 (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 $3240, then the time = ¹/₄₀₅ × 3240 years

= ^{1 × 3240}/₄₀₅ years

= ³²⁴⁰/₄₀₅ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

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

(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(4) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.

(6) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 3% simple interest?

(7) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?

(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11880 to clear the loan, then find the time period of the loan.

(9) Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.