Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $10370

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 = $10370 – $6100 = $4270

Thus, Simple Interest = $4270

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 × 4270}/_{6100 × 10}

= ⁴²⁷⁰⁰⁰/₆₁₀₀₀

= 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) = $6100

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

Simple Interest = $4270 (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 $6100

= ¹⁰/₁₀₀ × 6100

= ^{10 × 6100}/₁₀₀

= ⁶¹⁰⁰⁰/₁₀₀ = 610

Thus, simple Interest for 1 year = $610

Now,

∵ If the simple Interest is $610, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₁₀ years

∴ If the simple Interest is $4270, then the time = ¹/₆₁₀ × 4270 years

= ^{1 × 4270}/₆₁₀ years

= ⁴²⁷⁰/₆₁₀ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(2) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?

(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 4 years.

(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9280 to clear the loan, then find the time period of the loan.

(6) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(7) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.

(9) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.

(10) If Lisa paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.