Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $9360

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 = $9360 – $6000 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{6000 × 8}

= ³³⁶⁰⁰⁰/₄₈₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 8% per annum

Simple Interest = $3360 (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 $6000

= ⁸/₁₀₀ × 6000

= ^{8 × 6000}/₁₀₀

= ⁴⁸⁰⁰⁰/₁₀₀ = 480

Thus, simple Interest for 1 year = $480

Now,

∵ If the simple Interest is $480, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₈₀ × 3360 years

= ^{1 × 3360}/₄₈₀ years

= ³³⁶⁰/₄₈₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?

(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 3% simple interest for 4 years.

(3) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(5) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 3 years.

(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.

(9) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.