Simple Interest
Math MCQs

Question :    Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4900

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

Amount (A) = $9310

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 = $9310 – $4900 = $4410

Thus, Simple Interest = $4410

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 × 4410}/_{4900 × 10}

= ⁴⁴¹⁰⁰⁰/₄₉₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = 10% per annum

Simple Interest = $4410 (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 $4900

= ¹⁰/₁₀₀ × 4900

= ^{10 × 4900}/₁₀₀

= ⁴⁹⁰⁰⁰/₁₀₀ = 490

Thus, simple Interest for 1 year = $490

Now,

∵ If the simple Interest is $490, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₀ years

∴ If the simple Interest is $4410, then the time = ¹/₄₉₀ × 4410 years

= ^{1 × 4410}/₄₉₀ years

= ⁴⁴¹⁰/₄₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 5% simple interest.

(2) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 4 years.

(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

(4) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7964 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 9% simple interest?

(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?

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

(8) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(9) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 10% simple interest?

(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.