Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $7000

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

Amount (A) = $12670

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 = $12670 – $7000 = $5670

Thus, Simple Interest = $5670

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 × 5670}/_{7000 × 9}

= ⁵⁶⁷⁰⁰⁰/₆₃₀₀₀

= 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) = $7000

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

Simple Interest = $5670 (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 $7000

= ⁹/₁₀₀ × 7000

= ^{9 × 7000}/₁₀₀

= ⁶³⁰⁰⁰/₁₀₀ = 630

Thus, simple Interest for 1 year = $630

Now,

∵ If the simple Interest is $630, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₃₀ years

∴ If the simple Interest is $5670, then the time = ¹/₆₃₀ × 5670 years

= ^{1 × 5670}/₆₃₀ years

= ⁵⁶⁷⁰/₆₃₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.

(2) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?

(3) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.

(4) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.

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

(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(7) 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?

(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.

(10) Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.