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 $9184 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5600

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

Amount (A) = $9184

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 = $9184 – $5600 = $3584

Thus, Simple Interest = $3584

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 × 3584}/_{5600 × 8}

= ³⁵⁸⁴⁰⁰/₄₄₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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 = $3584 (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 $3584, then the time = ¹/₄₄₈ × 3584 years

= ^{1 × 3584}/₄₄₈ years

= ³⁵⁸⁴/₄₄₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.

(2) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(4) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.

(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?

(6) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.

(8) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?

(10) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.