Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 7% 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  8

Solution & Explanation

Solution

Given,

Principal (P) = $6000

Rate of Simple Interest (R) = 7% 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 × 7}

= ³³⁶⁰⁰⁰/₄₂₀₀₀

= 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) = $6000

Rate of Simple Interest (R) = 7% 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 = 7% of Principal

= 7% of $6000

= ⁷/₁₀₀ × 6000

= ^{7 × 6000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₂₀ × 3360 years

= ^{1 × 3360}/₄₂₀ years

= ³³⁶⁰/₄₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

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

(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.

(3) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.

(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.

(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?

(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(8) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?

(9) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8642 to clear the loan, then find the time period of the loan.

(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?