Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $10830

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 = $10830 – $5700 = $5130

Thus, Simple Interest = $5130

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 × 5130}/_{5700 × 9}

= ⁵¹³⁰⁰⁰/₅₁₃₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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) = $5700

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

Simple Interest = $5130 (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 $5700

= ⁹/₁₀₀ × 5700

= ^{9 × 5700}/₁₀₀

= ⁵¹³⁰⁰/₁₀₀ = 513

Thus, simple Interest for 1 year = $513

Now,

∵ If the simple Interest is $513, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₁₃ years

∴ If the simple Interest is $5130, then the time = ¹/₅₁₃ × 5130 years

= ^{1 × 5130}/₅₁₃ years

= ⁵¹³⁰/₅₁₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

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

(2) 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.

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?

(4) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(5) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6552 to clear the loan, then find the time period of the loan.

(6) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

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

(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.

(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 2% simple interest.

(10) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.