Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 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) = 8% per annum

Amount (A) = $8820

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 = $8820 – $4900 = $3920

Thus, Simple Interest = $3920

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 × 3920}/_{4900 × 8}

= ³⁹²⁰⁰⁰/₃₉₂₀₀

= 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) = 8% per annum

Simple Interest = $3920 (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 = 8% of Principal

= 8% of $4900

= ⁸/₁₀₀ × 4900

= ^{8 × 4900}/₁₀₀

= ³⁹²⁰⁰/₁₀₀ = 392

Thus, simple Interest for 1 year = $392

Now,

∵ If the simple Interest is $392, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₉₂ years

∴ If the simple Interest is $3920, then the time = ¹/₃₉₂ × 3920 years

= ^{1 × 3920}/₃₉₂ years

= ³⁹²⁰/₃₉₂ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.

(5) Sandra had to pay $5117.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) In how much time a principal of $3150 will amount to $3528 at a simple interest of 3% per annum?

(7) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.

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