Simple Interest
Math MCQs

Question :    Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $9632

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 = $9632 – $5600 = $4032

Thus, Simple Interest = $4032

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 × 4032}/_{5600 × 8}

= ⁴⁰³²⁰⁰/₄₄₈₀₀

= 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) = $5600

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

Simple Interest = $4032 (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 $5600

= ⁸/₁₀₀ × 5600

= ^{8 × 5600}/₁₀₀

= ⁴⁴⁸⁰⁰/₁₀₀ = 448

Thus, simple Interest for 1 year = $448

Now,

∵ If the simple Interest is $448, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₈ years

∴ If the simple Interest is $4032, then the time = ¹/₄₄₈ × 4032 years

= ^{1 × 4032}/₄₄₈ years

= ⁴⁰³²/₄₄₈ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.

(2) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 3 years.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.

(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.

(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.

(6) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(7) If John paid $3456 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(8) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.

(9) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?