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) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?

(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.

(3) How much loan did Melissa borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8820 to clear it?

(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.

(5) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?

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

(7) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.

(8) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 9% simple interest?

(10) Calculate the amount due if Karen borrowed a sum of $3950 at 3% simple interest for 3 years.