Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 10% 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  6

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 10% 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 × 10}

= ⁴⁰⁸⁰⁰⁰/₆₈₀₀₀

= 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) = 10% 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 = 10% of Principal

= 10% of $6800

= ¹⁰/₁₀₀ × 6800

= ^{10 × 6800}/₁₀₀

= ⁶⁸⁰⁰⁰/₁₀₀ = 680

Thus, simple Interest for 1 year = $680

Now,

∵ If the simple Interest is $680, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₈₀ years

∴ If the simple Interest is $4080, then the time = ¹/₆₈₀ × 4080 years

= ^{1 × 4080}/₆₈₀ years

= ⁴⁰⁸⁰/₆₈₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(2) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.

(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?

(4) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.

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

(6) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.

(7) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.

(8) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.