Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7661

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 = $7661 – $4700 = $2961

Thus, Simple Interest = $2961

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 × 2961}/_{4700 × 9}

= ²⁹⁶¹⁰⁰/₄₂₃₀₀

= 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) = $4700

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

Simple Interest = $2961 (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 $4700

= ⁹/₁₀₀ × 4700

= ^{9 × 4700}/₁₀₀

= ⁴²³⁰⁰/₁₀₀ = 423

Thus, simple Interest for 1 year = $423

Now,

∵ If the simple Interest is $423, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₃ years

∴ If the simple Interest is $2961, then the time = ¹/₄₂₃ × 2961 years

= ^{1 × 2961}/₄₂₃ years

= ²⁹⁶¹/₄₂₃ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(5) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.

(6) How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?

(7) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.

(8) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?

(9) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.