Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $8970

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

$8970 = P (1 + 3% × 5)

⇒ $8970 = P (1 + ³/₁₀₀ × 5)

⇒ $8970 = P (1 + ^{3 × 5}/₁₀₀)

⇒ $8970 = P (1 + ¹⁵/₁₀₀)

⇒ $8970 = P (^{100 + 15}/₁₀₀)

⇒ $8970 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $8970

⇒ P = ⁸⁹⁷⁰/_¹¹⁵/100

⇒ P = 8970 × ¹⁰⁰/₁₁₅

⇒ P = ^{8970 × 100}/₁₁₅

⇒ P = ⁸⁹⁷⁰⁰⁰/₁₁₅

⇒ P = $7800

Thus, the sum borrowed (P) = $7800 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 8970, then the Principal = ¹⁰⁰/₁₁₅ × 8970

= ^{100 × 8970}/₁₁₅

= ⁸⁹⁷⁰⁰⁰/₁₁₅

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.

(2) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.

(5) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.

(6) Charles had to pay $4251 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(7) What amount does David have to pay after 5 years if he takes a loan of $3400 at 6% simple interest?

(8) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?

(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.

(10) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?