Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9020

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 = $9020 – $5500 = $3520

Thus, Simple Interest = $3520

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 × 3520}/_{5500 × 8}

= ³⁵²⁰⁰⁰/₄₄₀₀₀

= 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) = $5500

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $3520 (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 = 8% of Principal

= 8% of $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $3520, then the time = ¹/₄₄₀ × 3520 years

= ^{1 × 3520}/₄₄₀ years

= ³⁵²⁰/₄₄₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?

(3) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.

(4) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if Richard borrowed a sum of $3600 at 9% simple interest for 3 years.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.

(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.