Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $9750

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

$9750 = P (1 + 5% × 5)

⇒ $9750 = P (1 + ⁵/₁₀₀ × 5)

⇒ $9750 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $9750 = P (1 + ²⁵/₁₀₀)

⇒ $9750 = P (^{100 + 25}/₁₀₀)

⇒ $9750 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $9750

⇒ P = ⁹⁷⁵⁰/_¹²⁵/100

⇒ P = 9750 × ¹⁰⁰/₁₂₅

⇒ P = ^{9750 × 100}/₁₂₅

⇒ P = ⁹⁷⁵⁰⁰⁰/₁₂₅

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 9750, then the Principal = ¹⁰⁰/₁₂₅ × 9750

= ^{100 × 9750}/₁₂₅

= ⁹⁷⁵⁰⁰⁰/₁₂₅

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?

(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.

(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.

(5) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?

(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?

(8) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?

(9) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.