Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $6880

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 = $6880 – $4000 = $2880

Thus, Simple Interest = $2880

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 × 2880}/_{4000 × 8}

= ²⁸⁸⁰⁰⁰/₃₂₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4000

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

Simple Interest = $2880 (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 $4000

= ⁸/₁₀₀ × 4000

= ^{8 × 4000}/₁₀₀

= ³²⁰⁰⁰/₁₀₀ = 320

Thus, simple Interest for 1 year = $320

Now,

∵ If the simple Interest is $320, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₀ years

∴ If the simple Interest is $2880, then the time = ¹/₃₂₀ × 2880 years

= ^{1 × 2880}/₃₂₀ years

= ²⁸⁸⁰/₃₂₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(2) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 8 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 8 years.

(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(7) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(8) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(9) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?