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 $8640 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5400

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

Amount (A) = $8640

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 = $8640 – $5400 = $3240

Thus, Simple Interest = $3240

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 × 3240}/_{5400 × 6}

= ³²⁴⁰⁰⁰/₃₂₄₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3240 (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 $3240, then the time = ¹/₃₂₄ × 3240 years

= ^{1 × 3240}/₃₂₄ years

= ³²⁴⁰/₃₂₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?

(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.

(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.

(4) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(5) If Kimberly paid $5022 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(8) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.

(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?