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 $10880 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10880

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 = $10880 – $6800 = $4080

Thus, Simple Interest = $4080

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 × 4080}/_{6800 × 6}

= ⁴⁰⁸⁰⁰⁰/₄₀₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $4080 (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 $4080, then the time = ¹/₄₀₈ × 4080 years

= ^{1 × 4080}/₄₀₈ years

= ⁴⁰⁸⁰/₄₀₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 3% simple interest?

(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(3) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?

(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 2% simple interest.

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

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.

(8) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.

(9) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(10) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?