Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $9248

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 = $9248 – $6800 = $2448

Thus, Simple Interest = $2448

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 × 2448}/_{6800 × 6}

= ²⁴⁴⁸⁰⁰/₄₀₈₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6800

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

Simple Interest = $2448 (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 $6800

= ⁶/₁₀₀ × 6800

= ^{6 × 6800}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $2448, then the time = ¹/₄₀₈ × 2448 years

= ^{1 × 2448}/₄₀₈ years

= ²⁴⁴⁸/₄₀₈ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 4 years.

(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 9% simple interest?

(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.

(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.

(7) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.

(8) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.

(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.

(10) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?