Simple Interest
Math MCQs

Question :    How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?

Correct Answer  $7800

Solution & Explanation

Solution

Given,

Amount (A) = $9360

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

$9360 = P (1 + 4% × 5)

⇒ $9360 = P (1 + ⁴/₁₀₀ × 5)

⇒ $9360 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $9360 = P (1 + ²⁰/₁₀₀)

⇒ $9360 = P (^{100 + 20}/₁₀₀)

⇒ $9360 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $9360

⇒ P = ⁹³⁶⁰/_¹²⁰/100

⇒ P = 9360 × ¹⁰⁰/₁₂₀

⇒ P = ^{9360 × 100}/₁₂₀

⇒ P = ⁹³⁶⁰⁰⁰/₁₂₀

⇒ 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 = 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 9360, then the Principal = ¹⁰⁰/₁₂₀ × 9360

= ^{100 × 9360}/₁₂₀

= ⁹³⁶⁰⁰⁰/₁₂₀

= 7800

Thus, Principal = $7800

Thus, the sum borrowed = $7800 Answer

Similar Questions

(1) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 7% simple interest?

(2) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.

(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 8 years.

(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.

(5) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(6) What amount does John have to pay after 6 years if he takes a loan of $3200 at 6% simple interest?

(7) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.

(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7708 to clear the loan, then find the time period of the loan.

(9) Thomas had to pay $4142 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?