Simple Interest
Math MCQs

Question :    James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4000

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

Amount (A) = $7600

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 = $7600 – $4000 = $3600

Thus, Simple Interest = $3600

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 × 3600}/_{4000 × 10}

= ³⁶⁰⁰⁰⁰/₄₀₀₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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) = $4000

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

Simple Interest = $3600 (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 $4000

= ¹⁰/₁₀₀ × 4000

= ^{10 × 4000}/₁₀₀

= ⁴⁰⁰⁰⁰/₁₀₀ = 400

Thus, simple Interest for 1 year = $400

Now,

∵ If the simple Interest is $400, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₀₀ years

∴ If the simple Interest is $3600, then the time = ¹/₄₀₀ × 3600 years

= ^{1 × 3600}/₄₀₀ years

= ³⁶⁰⁰/₄₀₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.

(2) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 3% simple interest.

(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(7) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?