Simple Interest
Math MCQs

Question :    Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6200

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

Amount (A) = $8804

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 = $8804 – $6200 = $2604

Thus, Simple Interest = $2604

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 × 2604}/_{6200 × 7}

= ²⁶⁰⁴⁰⁰/₄₃₄₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $6200

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

Simple Interest = $2604 (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 $6200

= ⁷/₁₀₀ × 6200

= ^{7 × 6200}/₁₀₀

= ⁴³⁴⁰⁰/₁₀₀ = 434

Thus, simple Interest for 1 year = $434

Now,

∵ If the simple Interest is $434, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₃₄ years

∴ If the simple Interest is $2604, then the time = ¹/₄₃₄ × 2604 years

= ^{1 × 2604}/₄₃₄ years

= ²⁶⁰⁴/₄₃₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 4% simple interest.

(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.

(4) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(5) Andrew had to pay $5376 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.

(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.

(8) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?

(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.

(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.