Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $10450

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 = $10450 – $5500 = $4950

Thus, Simple Interest = $4950

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 × 4950}/_{5500 × 9}

= ⁴⁹⁵⁰⁰⁰/₄₉₅₀₀

= 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) = $5500

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $4950 (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 = 9% of Principal

= 9% of $5500

= ⁹/₁₀₀ × 5500

= ^{9 × 5500}/₁₀₀

= ⁴⁹⁵⁰⁰/₁₀₀ = 495

Thus, simple Interest for 1 year = $495

Now,

∵ If the simple Interest is $495, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₉₅ years

∴ If the simple Interest is $4950, then the time = ¹/₄₉₅ × 4950 years

= ^{1 × 4950}/₄₉₅ years

= ⁴⁹⁵⁰/₄₉₅ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 5% simple interest.

(3) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 7 years.

(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 7% simple interest for 8 years.

(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.

(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?

(7) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8316 to clear the loan, then find the time period of the loan.

(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 7 years.

(9) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?