Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5500

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

Amount (A) = $9900

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 = $9900 – $5500 = $4400

Thus, Simple Interest = $4400

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 × 4400}/_{5500 × 10}

= ⁴⁴⁰⁰⁰⁰/₅₅₀₀₀

= 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) = $5500

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

Simple Interest = $4400 (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 $5500

= ¹⁰/₁₀₀ × 5500

= ^{10 × 5500}/₁₀₀

= ⁵⁵⁰⁰⁰/₁₀₀ = 550

Thus, simple Interest for 1 year = $550

Now,

∵ If the simple Interest is $550, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₅₀ years

∴ If the simple Interest is $4400, then the time = ¹/₅₅₀ × 4400 years

= ^{1 × 4400}/₅₅₀ years

= ⁴⁴⁰⁰/₅₅₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.

(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9230 to clear the loan, then find the time period of the loan.

(3) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?

(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.

(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.

(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.

(10) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.