Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $6900

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

$6900 = P (1 + 4% × 5)

⇒ $6900 = P (1 + ⁴/₁₀₀ × 5)

⇒ $6900 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $6900 = P (1 + ²⁰/₁₀₀)

⇒ $6900 = P (^{100 + 20}/₁₀₀)

⇒ $6900 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $6900

⇒ P = ⁶⁹⁰⁰/_¹²⁰/100

⇒ P = 6900 × ¹⁰⁰/₁₂₀

⇒ P = ^{6900 × 100}/₁₂₀

⇒ P = ⁶⁹⁰⁰⁰⁰/₁₂₀

⇒ P = $5750

Thus, the sum borrowed (P) = $5750 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 6900, then the Principal = ¹⁰⁰/₁₂₀ × 6900

= ^{100 × 6900}/₁₂₀

= ⁶⁹⁰⁰⁰⁰/₁₂₀

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.

(2) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?

(3) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?

(6) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?

(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.

(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.

(10) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?