Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7661

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 = $7661 – $4700 = $2961

Thus, Simple Interest = $2961

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 × 2961}/_{4700 × 9}

= ²⁹⁶¹⁰⁰/₄₂₃₀₀

= 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) = $4700

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

Simple Interest = $2961 (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 $4700

= ⁹/₁₀₀ × 4700

= ^{9 × 4700}/₁₀₀

= ⁴²³⁰⁰/₁₀₀ = 423

Thus, simple Interest for 1 year = $423

Now,

∵ If the simple Interest is $423, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₃ years

∴ If the simple Interest is $2961, then the time = ¹/₄₂₃ × 2961 years

= ^{1 × 2961}/₄₂₃ years

= ²⁹⁶¹/₄₂₃ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?

(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.

(4) How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?

(5) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.

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

(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.

(8) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(9) Calculate the amount due if Karen borrowed a sum of $3950 at 8% simple interest for 4 years.

(10) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.