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) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.

(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.

(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?

(9) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.

(10) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.