Simple Interest
Math MCQs

Question :    How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?

Correct Answer  $5750

Solution & Explanation

Solution

Given,

Amount (A) = $7187.5

Rate of Simple Interest (R) = 5%

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

$7187.5 = P (1 + 5% × 5)

⇒ $7187.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7187.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7187.5 = P (1 + ²⁵/₁₀₀)

⇒ $7187.5 = P (^{100 + 25}/₁₀₀)

⇒ $7187.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7187.5

⇒ P = ^7187.5/_¹²⁵/100

⇒ P = 7187.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{7187.5 × 100}/₁₂₅

⇒ P = ⁷¹⁸⁷⁵⁰/₁₂₅

⇒ 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

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 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7187.5, then the Principal = ¹⁰⁰/₁₂₅ × 7187.5

= ^{100 × 7187.5}/₁₂₅

= ⁷¹⁸⁷⁵⁰/₁₂₅

= 5750

Thus, Principal = $5750

Thus, the sum borrowed = $5750 Answer

Similar Questions

(1) If Margaret paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.

(3) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.

(4) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9412 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.

(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?

(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.

(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?

(10) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?