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) In how much time a principal of $3050 will amount to $3812.5 at a simple interest of 5% per annum?

(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $10780 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.

(4) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.

(6) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.

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

(8) Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(9) Donald had to pay $4770 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.