Simple Interest
MCQs Math

Question:     Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution And Explanation

Solution

Given,

Principal (P) = $5100

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $7242

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 = $7242 – $5100 = $2142

Thus, Simple Interest = $2142

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 × 2142}/_{5100 × 6}

= ²¹⁴²⁰⁰/₃₀₆₀₀

= 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) = $5100

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2142 (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 = 6% of Principal

= 6% of $5100

= ⁶/₁₀₀ × 5100

= ^{6 × 5100}/₁₀₀

= ³⁰⁶⁰⁰/₁₀₀ = 306

Thus, simple Interest for 1 year = $306

Now,

∵ If the simple Interest is $306, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₀₆ years

∴ If the simple Interest is $2142, then the time = ¹/₃₀₆ × 2142 years

= ^{1 × 2142}/₃₀₆ years

= ²¹⁴²/₃₀₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.

(3) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?

(5) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 4 years.

(6) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(7) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.

(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.

(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?

(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 7 years.