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 $9440 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $9440

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 = $9440 – $5900 = $3540

Thus, Simple Interest = $3540

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 × 3540}/_{5900 × 10}

= ³⁵⁴⁰⁰⁰/₅₉₀₀₀

= 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) = $5900

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

Simple Interest = $3540 (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 $3540, then the time = ¹/₅₉₀ × 3540 years

= ^{1 × 3540}/₅₉₀ years

= ³⁵⁴⁰/₅₉₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.

(3) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(4) If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(5) If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(7) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.

(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.

(10) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 5% simple interest?