Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $5800

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9454

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 = $9454 – $5800 = $3654

Thus, Simple Interest = $3654

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 × 3654}/_{5800 × 9}

= ³⁶⁵⁴⁰⁰/₅₂₂₀₀

= 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) = $5800

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3654 (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 = 9% of Principal

= 9% of $5800

= ⁹/₁₀₀ × 5800

= ^{9 × 5800}/₁₀₀

= ⁵²²⁰⁰/₁₀₀ = 522

Thus, simple Interest for 1 year = $522

Now,

∵ If the simple Interest is $522, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₂ years

∴ If the simple Interest is $3654, then the time = ¹/₅₂₂ × 3654 years

= ^{1 × 3654}/₅₂₂ years

= ³⁶⁵⁴/₅₂₂ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.

(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.

(4) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(5) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 7 years.

(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.

(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if Susan borrowed a sum of $3650 at 10% simple interest for 4 years.