Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4900

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $8330

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 = $8330 – $4900 = $3430

Thus, Simple Interest = $3430

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 × 3430}/_{4900 × 7}

= ³⁴³⁰⁰⁰/₃₄₃₀₀

= 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) = $4900

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3430 (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 = 7% of Principal

= 7% of $4900

= ⁷/₁₀₀ × 4900

= ^{7 × 4900}/₁₀₀

= ³⁴³⁰⁰/₁₀₀ = 343

Thus, simple Interest for 1 year = $343

Now,

∵ If the simple Interest is $343, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₄₃ years

∴ If the simple Interest is $3430, then the time = ¹/₃₄₃ × 3430 years

= ^{1 × 3430}/₃₄₃ years

= ³⁴³⁰/₃₄₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 8 years.

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

(3) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.

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

(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.

(7) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?

(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.

(9) Kimberly had to pay $4929 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 if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.