Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9976 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $9976

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 = $9976 – $5800 = $4176

Thus, Simple Interest = $4176

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 × 4176}/_{5800 × 8}

= ⁴¹⁷⁶⁰⁰/₄₆₄₀₀

= 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) = $5800

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

Simple Interest = $4176 (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 $5800

= ⁸/₁₀₀ × 5800

= ^{8 × 5800}/₁₀₀

= ⁴⁶⁴⁰⁰/₁₀₀ = 464

Thus, simple Interest for 1 year = $464

Now,

∵ If the simple Interest is $464, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₄ years

∴ If the simple Interest is $4176, then the time = ¹/₄₆₄ × 4176 years

= ^{1 × 4176}/₄₆₄ years

= ⁴¹⁷⁶/₄₆₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.

(2) Jessica had to pay $3975 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.

(4) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.

(7) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?

(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(9) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(10) Michelle had to pay $5395.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.