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 $9760 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9760

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 = $9760 – $6100 = $3660

Thus, Simple Interest = $3660

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 × 3660}/_{6100 × 10}

= ³⁶⁶⁰⁰⁰/₆₁₀₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $3660 (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 $3660, then the time = ¹/₆₁₀ × 3660 years

= ^{1 × 3660}/₆₁₀ years

= ³⁶⁶⁰/₆₁₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.

(2) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?

(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(4) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(5) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 3 years.

(6) If Elizabeth paid $4140 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 4 years.

(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.

(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.