Simple Interest
Math MCQs

Question :    How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?

Correct Answer  $6000

Solution & Explanation

Solution

Given,

Amount (A) = $7200

Rate of Simple Interest (R) = 4%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$7200 = P (1 + 4% × 5)

⇒ $7200 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7200 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7200 = P (1 + ²⁰/₁₀₀)

⇒ $7200 = P (^{100 + 20}/₁₀₀)

⇒ $7200 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7200

⇒ P = ⁷²⁰⁰/_¹²⁰/100

⇒ P = 7200 × ¹⁰⁰/₁₂₀

⇒ P = ^{7200 × 100}/₁₂₀

⇒ P = ⁷²⁰⁰⁰⁰/₁₂₀

⇒ P = $6000

Thus, the sum borrowed (P) = $6000 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 7200, then the Principal = ¹⁰⁰/₁₂₀ × 7200

= ^{100 × 7200}/₁₂₀

= ⁷²⁰⁰⁰⁰/₁₂₀

= 6000

Thus, Principal = $6000

Thus, the sum borrowed = $6000 Answer

Similar Questions

(1) If William paid $3920 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.

(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 3% simple interest.

(4) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.

(5) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.

(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.

(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 9% simple interest?

(8) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 9% simple interest?

(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 7% simple interest?

(10) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.