Simple Interest
Math MCQs

Question :    Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6800

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $10608

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 = $10608 – $6800 = $3808

Thus, Simple Interest = $3808

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 × 3808}/_{6800 × 8}

= ³⁸⁰⁸⁰⁰/₅₄₄₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 8% per annum

Simple Interest = $3808 (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 = 8% of Principal

= 8% of $6800

= ⁸/₁₀₀ × 6800

= ^{8 × 6800}/₁₀₀

= ⁵⁴⁴⁰⁰/₁₀₀ = 544

Thus, simple Interest for 1 year = $544

Now,

∵ If the simple Interest is $544, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₄ years

∴ If the simple Interest is $3808, then the time = ¹/₅₄₄ × 3808 years

= ^{1 × 3808}/₅₄₄ years

= ³⁸⁰⁸/₅₄₄ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.

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

(3) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.

(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.

(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6520 to clear the loan, then find the time period of the loan.

(8) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.

(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.

(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8493 to clear the loan, then find the time period of the loan.