Simple Interest
Math MCQs

Question :    How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?

Correct Answer  $7750

Solution & Explanation

Solution

Given,

Amount (A) = $8912.5

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

$8912.5 = P (1 + 3% × 5)

⇒ $8912.5 = P (1 + ³/₁₀₀ × 5)

⇒ $8912.5 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8912.5 = P (1 + ¹⁵/₁₀₀)

⇒ $8912.5 = P (^{100 + 15}/₁₀₀)

⇒ $8912.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8912.5

⇒ P = ^8912.5/_¹¹⁵/100

⇒ P = 8912.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{8912.5 × 100}/₁₁₅

⇒ P = ⁸⁹¹²⁵⁰/₁₁₅

⇒ P = $7750

Thus, the sum borrowed (P) = $7750 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 8912.5, then the Principal = ¹⁰⁰/₁₁₅ × 8912.5

= ^{100 × 8912.5}/₁₁₅

= ⁸⁹¹²⁵⁰/₁₁₅

= 7750

Thus, Principal = $7750

Thus, the sum borrowed = $7750 Answer

Similar Questions

(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 7 years.

(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.

(3) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 7 years.

(4) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(5) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(7) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 7 years.

(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?

(9) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(10) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.