Simple Interest
Math MCQs

Question :    Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $6000

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

Amount (A) = $10320

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 = $10320 – $6000 = $4320

Thus, Simple Interest = $4320

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 × 4320}/_{6000 × 9}

= ⁴³²⁰⁰⁰/₅₄₀₀₀

= 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) = $6000

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

Simple Interest = $4320 (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 $6000

= ⁹/₁₀₀ × 6000

= ^{9 × 6000}/₁₀₀

= ⁵⁴⁰⁰⁰/₁₀₀ = 540

Thus, simple Interest for 1 year = $540

Now,

∵ If the simple Interest is $540, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₀ years

∴ If the simple Interest is $4320, then the time = ¹/₅₄₀ × 4320 years

= ^{1 × 4320}/₅₄₀ years

= ⁴³²⁰/₅₄₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(2) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.

(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?

(4) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?

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

(6) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?

(8) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 3 years.

(10) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.