Simple Interest
Math MCQs

Question :    Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5100

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

Amount (A) = $9180

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 = $9180 – $5100 = $4080

Thus, Simple Interest = $4080

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 × 4080}/_{5100 × 8}

= ⁴⁰⁸⁰⁰⁰/₄₀₈₀₀

= 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) = $5100

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

Simple Interest = $4080 (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 $5100

= ⁸/₁₀₀ × 5100

= ^{8 × 5100}/₁₀₀

= ⁴⁰⁸⁰⁰/₁₀₀ = 408

Thus, simple Interest for 1 year = $408

Now,

∵ If the simple Interest is $408, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₈ years

∴ If the simple Interest is $4080, then the time = ¹/₄₀₈ × 4080 years

= ^{1 × 4080}/₄₀₈ years

= ⁴⁰⁸⁰/₄₀₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9632 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(4) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?

(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.

(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.

(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(10) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.