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 $11900 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $11900

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 = $11900 – $7000 = $4900

Thus, Simple Interest = $4900

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 × 4900}/_{7000 × 10}

= ⁴⁹⁰⁰⁰⁰/₇₀₀₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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 = $4900 (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 $4900, then the time = ¹/₇₀₀ × 4900 years

= ^{1 × 4900}/₇₀₀ years

= ⁴⁹⁰⁰/₇₀₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

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

(3) How much loan did Sharon borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9300 to clear it?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.

(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(10) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.