Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $9798

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 = $9798 – $6900 = $2898

Thus, Simple Interest = $2898

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 × 2898}/_{6900 × 7}

= ²⁸⁹⁸⁰⁰/₄₈₃₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $2898 (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 = 7% of Principal

= 7% of $6900

= ⁷/₁₀₀ × 6900

= ^{7 × 6900}/₁₀₀

= ⁴⁸³⁰⁰/₁₀₀ = 483

Thus, simple Interest for 1 year = $483

Now,

∵ If the simple Interest is $483, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₃ years

∴ If the simple Interest is $2898, then the time = ¹/₄₈₃ × 2898 years

= ^{1 × 2898}/₄₈₃ years

= ²⁸⁹⁸/₄₈₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.

(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(5) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(6) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.

(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.

(9) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.