Simple Interest
Math MCQs

Question :    How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?

Correct Answer  $7950

Solution & Explanation

Solution

Given,

Amount (A) = $9142.5

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

$9142.5 = P (1 + 3% × 5)

⇒ $9142.5 = P (1 + ³/₁₀₀ × 5)

⇒ $9142.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $9142.5 = P (1 + ¹⁵/₁₀₀)

⇒ $9142.5 = P (^{100 + 15}/₁₀₀)

⇒ $9142.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $9142.5

⇒ P = ^9142.5/_¹¹⁵/100

⇒ P = 9142.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{9142.5 × 100}/₁₁₅

⇒ P = ⁹¹⁴²⁵⁰/₁₁₅

⇒ P = $7950

Thus, the sum borrowed (P) = $7950 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 9142.5, then the Principal = ¹⁰⁰/₁₁₅ × 9142.5

= ^{100 × 9142.5}/₁₁₅

= ⁹¹⁴²⁵⁰/₁₁₅

= 7950

Thus, Principal = $7950

Thus, the sum borrowed = $7950 Answer

Similar Questions

(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.

(2) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?

(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 5% simple interest?

(4) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.

(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) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.

(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.