Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $10620

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 = $10620 – $5900 = $4720

Thus, Simple Interest = $4720

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 × 4720}/_{5900 × 10}

= ⁴⁷²⁰⁰⁰/₅₉₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = 10% per annum

Simple Interest = $4720 (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 $5900

= ¹⁰/₁₀₀ × 5900

= ^{10 × 5900}/₁₀₀

= ⁵⁹⁰⁰⁰/₁₀₀ = 590

Thus, simple Interest for 1 year = $590

Now,

∵ If the simple Interest is $590, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₀ years

∴ If the simple Interest is $4720, then the time = ¹/₅₉₀ × 4720 years

= ^{1 × 4720}/₅₉₀ years

= ⁴⁷²⁰/₅₉₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.

(2) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?

(4) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.

(5) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(6) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

(8) If Daniel paid $4592 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?

(10) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.