Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $10030

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 = $10030 – $5900 = $4130

Thus, Simple Interest = $4130

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 × 4130}/_{5900 × 7}

= ⁴¹³⁰⁰⁰/₄₁₃₀₀

= 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) = $5900

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

Simple Interest = $4130 (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 $5900

= ⁷/₁₀₀ × 5900

= ^{7 × 5900}/₁₀₀

= ⁴¹³⁰⁰/₁₀₀ = 413

Thus, simple Interest for 1 year = $413

Now,

∵ If the simple Interest is $413, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₁₃ years

∴ If the simple Interest is $4130, then the time = ¹/₄₁₃ × 4130 years

= ^{1 × 4130}/₄₁₃ years

= ⁴¹³⁰/₄₁₃ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?

(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.

(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(4) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(5) Steven had to pay $5290 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(7) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.

(8) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.

(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.