Simple Interest
Math MCQs

Question :    How much loan did Ronald borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9000 to clear it?

Correct Answer  $7500

Solution & Explanation

Solution

Given,

Amount (A) = $9000

Rate of Simple Interest (R) = 4%

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

$9000 = P (1 + 4% × 5)

⇒ $9000 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9000 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9000 = P (1 + ²⁰/₁₀₀)

⇒ $9000 = P (^{100 + 20}/₁₀₀)

⇒ $9000 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9000

⇒ P = ⁹⁰⁰⁰/_¹²⁰/100

⇒ P = 9000 × ¹⁰⁰/₁₂₀

⇒ P = ^{9000 × 100}/₁₂₀

⇒ P = ⁹⁰⁰⁰⁰⁰/₁₂₀

⇒ P = $7500

Thus, the sum borrowed (P) = $7500 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 = 4% per annum

Thus, Interest = 4% of principal

⇒ Interest = 4% of 100 = 4

Thus, Simple Interest for 1 year = 4

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 × 4 = 20

Thus, simple interest for 5 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 9000, then the Principal = ¹⁰⁰/₁₂₀ × 9000

= ^{100 × 9000}/₁₂₀

= ⁹⁰⁰⁰⁰⁰/₁₂₀

= 7500

Thus, Principal = $7500

Thus, the sum borrowed = $7500 Answer

Similar Questions

(1) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?

(2) Emily had to pay $5035 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.

(4) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.

(5) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?

(6) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(7) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.

(8) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.

(9) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?

(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?