Simple Interest
Math MCQs

Question :    How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?

Correct Answer  $6150

Solution & Explanation

Solution

Given,

Amount (A) = $7072.5

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

$7072.5 = P (1 + 3% × 5)

⇒ $7072.5 = P (1 + ³/₁₀₀ × 5)

⇒ $7072.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $7072.5 = P (1 + ¹⁵/₁₀₀)

⇒ $7072.5 = P (^{100 + 15}/₁₀₀)

⇒ $7072.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $7072.5

⇒ P = ^7072.5/_¹¹⁵/100

⇒ P = 7072.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{7072.5 × 100}/₁₁₅

⇒ P = ⁷⁰⁷²⁵⁰/₁₁₅

⇒ P = $6150

Thus, the sum borrowed (P) = $6150 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 7072.5, then the Principal = ¹⁰⁰/₁₁₅ × 7072.5

= ^{100 × 7072.5}/₁₁₅

= ⁷⁰⁷²⁵⁰/₁₁₅

= 6150

Thus, Principal = $6150

Thus, the sum borrowed = $6150 Answer

Similar Questions

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

(2) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?

(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.

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

(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.

(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.

(7) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

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

(9) If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.