Simple Interest
Math MCQs

Question :    Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6600

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

Amount (A) = $9372

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 = $9372 – $6600 = $2772

Thus, Simple Interest = $2772

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 × 2772}/_{6600 × 7}

= ²⁷⁷²⁰⁰/₄₆₂₀₀

= 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) = $6600

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

Simple Interest = $2772 (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 $6600

= ⁷/₁₀₀ × 6600

= ^{7 × 6600}/₁₀₀

= ⁴⁶²⁰⁰/₁₀₀ = 462

Thus, simple Interest for 1 year = $462

Now,

∵ If the simple Interest is $462, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₆₂ years

∴ If the simple Interest is $2772, then the time = ¹/₄₆₂ × 2772 years

= ^{1 × 2772}/₄₆₂ years

= ²⁷⁷²/₄₆₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.

(4) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?

(5) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.

(9) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?

(10) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.