Simple Interest
Math MCQs

Question :    Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4100

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

Amount (A) = $7790

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 = $7790 – $4100 = $3690

Thus, Simple Interest = $3690

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 × 3690}/_{4100 × 10}

= ³⁶⁹⁰⁰⁰/₄₁₀₀₀

= 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) = $4100

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

Simple Interest = $3690 (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 $4100

= ¹⁰/₁₀₀ × 4100

= ^{10 × 4100}/₁₀₀

= ⁴¹⁰⁰⁰/₁₀₀ = 410

Thus, simple Interest for 1 year = $410

Now,

∵ If the simple Interest is $410, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₀ years

∴ If the simple Interest is $3690, then the time = ¹/₄₁₀ × 3690 years

= ^{1 × 3690}/₄₁₀ years

= ³⁶⁹⁰/₄₁₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7650 to clear the loan, then find the time period of the loan.

(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(3) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 3 years.

(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.

(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.

(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.