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 Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?

(2) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?

(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 8% simple interest?

(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.

(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?

(7) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(8) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?

(9) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.