Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $14000 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $14000

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 = $14000 – $7000 = $7000

Thus, Simple Interest = $7000

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 × 7000}/_{7000 × 10}

= ⁷⁰⁰⁰⁰⁰/₇₀₀₀₀

= 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) = $7000

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

Simple Interest = $7000 (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 $7000

= ¹⁰/₁₀₀ × 7000

= ^{10 × 7000}/₁₀₀

= ⁷⁰⁰⁰⁰/₁₀₀ = 700

Thus, simple Interest for 1 year = $700

Now,

∵ If the simple Interest is $700, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₇₀₀ years

∴ If the simple Interest is $7000, then the time = ¹/₇₀₀ × 7000 years

= ^{1 × 7000}/₇₀₀ years

= ⁷⁰⁰⁰/₇₀₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?

(2) If Jessica paid $4200 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(3) In how much time a principal of $3150 will amount to $3339 at a simple interest of 3% per annum?

(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.

(5) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 7% simple interest for 8 years.

(7) If Linda paid $3752 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(8) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?

(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.