Simple Interest
Math MCQs

Question :    Jessica took a loan of $5500 at the rate of 8% 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  10

Solution & Explanation

Solution

Given,

Principal (P) = $5500

Rate of Simple Interest (R) = 8% 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 × 8}

= ⁴⁴⁰⁰⁰⁰/₄₄₀₀₀

= 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) = 8% 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 = 8% of Principal

= 8% of $5500

= ⁸/₁₀₀ × 5500

= ^{8 × 5500}/₁₀₀

= ⁴⁴⁰⁰⁰/₁₀₀ = 440

Thus, simple Interest for 1 year = $440

Now,

∵ If the simple Interest is $440, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₀ years

∴ If the simple Interest is $4400, then the time = ¹/₄₄₀ × 4400 years

= ^{1 × 4400}/₄₄₀ years

= ⁴⁴⁰⁰/₄₄₀ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.

(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7320 to clear it?

(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?

(5) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(7) William had to pay $3920 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(8) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.

(9) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.