Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $11480

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 = $11480 – $7000 = $4480

Thus, Simple Interest = $4480

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 × 4480}/_{7000 × 8}

= ⁴⁴⁸⁰⁰⁰/₅₆₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 8% per annum

Simple Interest = $4480 (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 = 8% of Principal

= 8% of $7000

= ⁸/₁₀₀ × 7000

= ^{8 × 7000}/₁₀₀

= ⁵⁶⁰⁰⁰/₁₀₀ = 560

Thus, simple Interest for 1 year = $560

Now,

∵ If the simple Interest is $560, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₆₀ years

∴ If the simple Interest is $4480, then the time = ¹/₅₆₀ × 4480 years

= ^{1 × 4480}/₅₆₀ years

= ⁴⁴⁸⁰/₅₆₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 10% simple interest.

(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?

(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

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

(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.

(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.

(9) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.

(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?