Simple Interest
Math MCQs

Question :    How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

Correct Answer  $6800

Solution & Explanation

Solution

Given,

Amount (A) = $8160

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

$8160 = P (1 + 4% × 5)

⇒ $8160 = P (1 + ⁴/₁₀₀ × 5)

⇒ $8160 = P (1 + ^{4 × 5}/₁₀₀)

⇒ $8160 = P (1 + ²⁰/₁₀₀)

⇒ $8160 = P (^{100 + 20}/₁₀₀)

⇒ $8160 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $8160

⇒ P = ⁸¹⁶⁰/_¹²⁰/100

⇒ P = 8160 × ¹⁰⁰/₁₂₀

⇒ P = ^{8160 × 100}/₁₂₀

⇒ P = ⁸¹⁶⁰⁰⁰/₁₂₀

⇒ P = $6800

Thus, the sum borrowed (P) = $6800 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 8160, then the Principal = ¹⁰⁰/₁₂₀ × 8160

= ^{100 × 8160}/₁₂₀

= ⁸¹⁶⁰⁰⁰/₁₂₀

= 6800

Thus, Principal = $6800

Thus, the sum borrowed = $6800 Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.

(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.

(3) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?

(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 7% simple interest?

(5) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(6) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9540 to clear it?

(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.

(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 10% simple interest?

(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.

(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.