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 $11946 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $11946

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 = $11946 – $6600 = $5346

Thus, Simple Interest = $5346

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 × 5346}/_{6600 × 9}

= ⁵³⁴⁶⁰⁰/₅₉₄₀₀

= 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) = $6600

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

Simple Interest = $5346 (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 $5346, then the time = ¹/₅₉₄ × 5346 years

= ^{1 × 5346}/₅₉₄ years

= ⁵³⁴⁶/₅₉₄ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.

(4) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(5) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?

(6) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.

(8) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?

(9) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) How much loan did Betty borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7187.5 to clear it?