Simple Interest
Math MCQs

Question :    How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?

Correct Answer  $5850

Solution & Explanation

Solution

Given,

Amount (A) = $6727.5

Rate of Simple Interest (R) = 3%

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

$6727.5 = P (1 + 3% × 5)

⇒ $6727.5 = P (1 + ³/₁₀₀ × 5)

⇒ $6727.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $6727.5 = P (1 + ¹⁵/₁₀₀)

⇒ $6727.5 = P (^{100 + 15}/₁₀₀)

⇒ $6727.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $6727.5

⇒ P = ^6727.5/_¹¹⁵/100

⇒ P = 6727.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{6727.5 × 100}/₁₁₅

⇒ P = ⁶⁷²⁷⁵⁰/₁₁₅

⇒ P = $5850

Thus, the sum borrowed (P) = $5850 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 15

Thus, simple interest for 5 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 6727.5, then the Principal = ¹⁰⁰/₁₁₅ × 6727.5

= ^{100 × 6727.5}/₁₁₅

= ⁶⁷²⁷⁵⁰/₁₁₅

= 5850

Thus, Principal = $5850

Thus, the sum borrowed = $5850 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.

(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.

(3) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.

(5) What amount does James have to pay after 6 years if he takes a loan of $3000 at 4% simple interest?

(6) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?

(7) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(8) William had to pay $4025 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8690 to clear it?

(10) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.