Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $8732

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 = $8732 – $5900 = $2832

Thus, Simple Interest = $2832

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 × 2832}/_{5900 × 6}

= ²⁸³²⁰⁰/₃₅₄₀₀

= 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) = $5900

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

Simple Interest = $2832 (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 $5900

= ⁶/₁₀₀ × 5900

= ^{6 × 5900}/₁₀₀

= ³⁵⁴⁰⁰/₁₀₀ = 354

Thus, simple Interest for 1 year = $354

Now,

∵ If the simple Interest is $354, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₅₄ years

∴ If the simple Interest is $2832, then the time = ¹/₃₅₄ × 2832 years

= ^{1 × 2832}/₃₅₄ years

= ²⁸³²/₃₅₄ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(2) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?

(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.

(4) How much loan did Mark borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8000 to clear it?

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.

(6) If Paul paid $5640 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $9010 to clear the loan, then find the time period of the loan.

(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.

(9) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.