Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $12540

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 = $12540 – $6600 = $5940

Thus, Simple Interest = $5940

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 × 5940}/_{6600 × 9}

= ⁵⁹⁴⁰⁰⁰/₅₉₄₀₀

= 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) = $6600

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

Simple Interest = $5940 (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 $6600

= ⁹/₁₀₀ × 6600

= ^{9 × 6600}/₁₀₀

= ⁵⁹⁴⁰⁰/₁₀₀ = 594

Thus, simple Interest for 1 year = $594

Now,

∵ If the simple Interest is $594, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₄ years

∴ If the simple Interest is $5940, then the time = ¹/₅₉₄ × 5940 years

= ^{1 × 5940}/₅₉₄ years

= ⁵⁹⁴⁰/₅₉₄ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(2) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 9% simple interest?

(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.

(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 10% simple interest?

(6) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.

(7) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 10% simple interest?

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 4% simple interest?

(9) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.