Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6200

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11780

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 = $11780 – $6200 = $5580

Thus, Simple Interest = $5580

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 × 5580}/_{6200 × 10}

= ⁵⁵⁸⁰⁰⁰/₆₂₀₀₀

= 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) = $6200

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $5580 (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 = 10% of Principal

= 10% of $6200

= ¹⁰/₁₀₀ × 6200

= ^{10 × 6200}/₁₀₀

= ⁶²⁰⁰⁰/₁₀₀ = 620

Thus, simple Interest for 1 year = $620

Now,

∵ If the simple Interest is $620, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₀ years

∴ If the simple Interest is $5580, then the time = ¹/₆₂₀ × 5580 years

= ^{1 × 5580}/₆₂₀ years

= ⁵⁵⁸⁰/₆₂₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) William had to pay $3710 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(4) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.

(6) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?

(7) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?

(8) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.

(9) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

(10) If Barbara paid $4260 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.