Simple Interest
Math MCQs

Question :    Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5400

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7992

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 = $7992 – $5400 = $2592

Thus, Simple Interest = $2592

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 × 2592}/_{5400 × 6}

= ²⁵⁹²⁰⁰/₃₂₄₀₀

= 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) = $5400

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2592 (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 = 6% of Principal

= 6% of $5400

= ⁶/₁₀₀ × 5400

= ^{6 × 5400}/₁₀₀

= ³²⁴⁰⁰/₁₀₀ = 324

Thus, simple Interest for 1 year = $324

Now,

∵ If the simple Interest is $324, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₂₄ years

∴ If the simple Interest is $2592, then the time = ¹/₃₂₄ × 2592 years

= ^{1 × 2592}/₃₂₄ years

= ²⁵⁹²/₃₂₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.

(3) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.

(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(5) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.

(6) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?

(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.

(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.