Simple Interest
Math MCQs

Question :    How much loan did Charles borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7080 to clear it?

Correct Answer  $5900

Solution & Explanation

Solution

Given,

Amount (A) = $7080

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

$7080 = P (1 + 4% × 5)

⇒ $7080 = P (1 + ⁴/₁₀₀ × 5)

⇒ $7080 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $7080 = P (1 + ²⁰/₁₀₀)

⇒ $7080 = P (^{100 + 20}/₁₀₀)

⇒ $7080 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $7080

⇒ P = ⁷⁰⁸⁰/_¹²⁰/100

⇒ P = 7080 × ¹⁰⁰/₁₂₀

⇒ P = ^{7080 × 100}/₁₂₀

⇒ P = ⁷⁰⁸⁰⁰⁰/₁₂₀

⇒ P = $5900

Thus, the sum borrowed (P) = $5900 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 7080, then the Principal = ¹⁰⁰/₁₂₀ × 7080

= ^{100 × 7080}/₁₂₀

= ⁷⁰⁸⁰⁰⁰/₁₂₀

= 5900

Thus, Principal = $5900

Thus, the sum borrowed = $5900 Answer

Similar Questions

(1) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 6% simple interest?

(2) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.

(3) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.

(4) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7647.5 to clear it?

(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.

(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?

(7) How much loan did Patricia borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6437.5 to clear it?

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 10% simple interest.

(9) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(10) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.