Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8236

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 = $8236 – $5800 = $2436

Thus, Simple Interest = $2436

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 × 2436}/_{5800 × 6}

= ²⁴³⁶⁰⁰/₃₄₈₀₀

= 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) = $5800

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

Simple Interest = $2436 (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 $5800

= ⁶/₁₀₀ × 5800

= ^{6 × 5800}/₁₀₀

= ³⁴⁸⁰⁰/₁₀₀ = 348

Thus, simple Interest for 1 year = $348

Now,

∵ If the simple Interest is $348, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₈ years

∴ If the simple Interest is $2436, then the time = ¹/₃₄₈ × 2436 years

= ^{1 × 2436}/₃₄₈ years

= ²⁴³⁶/₃₄₈ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?

(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.

(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(6) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6562.5 to clear it?

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?

(10) What amount does John have to pay after 6 years if he takes a loan of $3200 at 8% simple interest?