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) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 3 years.

(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.

(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 7 years.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.

(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?

(9) 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.

(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.