Simple Interest
Math MCQs

Question :    How much loan did Donald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7800 to clear it?

Correct Answer  $6500

Solution & Explanation

Solution

Given,

Amount (A) = $7800

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

$7800 = P (1 + 4% × 5)

⇒ $7800 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7800 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7800 = P (1 + ²⁰/₁₀₀)

⇒ $7800 = P (^{100 + 20}/₁₀₀)

⇒ $7800 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7800

⇒ P = ⁷⁸⁰⁰/_¹²⁰/100

⇒ P = 7800 × ¹⁰⁰/₁₂₀

⇒ P = ^{7800 × 100}/₁₂₀

⇒ P = ⁷⁸⁰⁰⁰⁰/₁₂₀

⇒ P = $6500

Thus, the sum borrowed (P) = $6500 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 7800, then the Principal = ¹⁰⁰/₁₂₀ × 7800

= ^{100 × 7800}/₁₂₀

= ⁷⁸⁰⁰⁰⁰/₁₂₀

= 6500

Thus, Principal = $6500

Thus, the sum borrowed = $6500 Answer

Similar Questions

(1) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.

(2) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(3) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(5) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?

(6) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 7 years.

(7) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(8) How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?

(9) If Nancy paid $4648 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 6% simple interest?