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 Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?

(2) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.

(4) Calculate the amount due if Linda borrowed a sum of $3350 at 6% simple interest for 3 years.

(5) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(7) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.

(8) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 3 years.