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 $12920 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) = 10% per annum

Amount (A) = $12920

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 = $12920 – $6800 = $6120

Thus, Simple Interest = $6120

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 × 6120}/_{6800 × 10}

= ⁶¹²⁰⁰⁰/₆₈₀₀₀

= 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) = 10% per annum

Simple Interest = $6120 (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 $6120, then the time = ¹/₆₈₀ × 6120 years

= ^{1 × 6120}/₆₈₀ years

= ⁶¹²⁰/₆₈₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?

(3) Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 7 years.

(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(9) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.