Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8520

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 = $8520 – $6000 = $2520

Thus, Simple Interest = $2520

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 × 2520}/_{6000 × 7}

= ²⁵²⁰⁰⁰/₄₂₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2520 (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 = 7% of Principal

= 7% of $6000

= ⁷/₁₀₀ × 6000

= ^{7 × 6000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $2520, then the time = ¹/₄₂₀ × 2520 years

= ^{1 × 2520}/₄₂₀ years

= ²⁵²⁰/₄₂₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.

(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.

(5) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) If Paul paid $5264 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.

(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.

(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.