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) In how much time a principal of $3200 will amount to $3392 at a simple interest of 2% per annum?

(2) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $7668 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(4) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?

(5) 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?

(6) In how much time a principal of $3000 will amount to $3480 at a simple interest of 4% per annum?

(7) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?

(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?

(10) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.