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 $10472 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6800

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

Amount (A) = $10472

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 = $10472 – $6800 = $3672

Thus, Simple Interest = $3672

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 × 3672}/_{6800 × 6}

= ³⁶⁷²⁰⁰/₄₀₈₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $3672 (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 $3672, then the time = ¹/₄₀₈ × 3672 years

= ^{1 × 3672}/₄₀₈ years

= ³⁶⁷²/₄₀₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.

(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 8% simple interest for 4 years.

(6) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.

(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(9) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.

(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.