Simple Interest
Math MCQs

Question :    If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4800

Solution & Explanation

Solution

Given,

Amount (A) = $5568

Rate of Simple Interest (R) = 4%

Time (T) = 4 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

$5568 = P (1 + 4% × 4)

⇒ $5568 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5568 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5568 = P (1 + ¹⁶/₁₀₀)

⇒ $5568 = P (^{100 + 16}/₁₀₀)

⇒ $5568 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5568

⇒ P = ⁵⁵⁶⁸/_¹¹⁶/100

⇒ P = 5568 × ¹⁰⁰/₁₁₆

⇒ P = ^{5568 × 100}/₁₁₆

⇒ P = ⁵⁵⁶⁸⁰⁰/₁₁₆

⇒ P = $4800

Thus, the sum borrowed (P) = $4800 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 4 = 16

Thus, simple interest for 4 years = 16

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 16 = 116

Calculation of the Principal

Now,

∵ If the Amount is 116, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₆

∴ If the Amount is 5568, then the Principal = ¹⁰⁰/₁₁₆ × 5568

= ^{100 × 5568}/₁₁₆

= ⁵⁵⁶⁸⁰⁰/₁₁₆

= 4800

Thus, Principal = $4800

Thus, the sum borrowed = $4800 Answer

Similar Questions

(1) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 3% simple interest?

(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?

(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.

(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.

(6) How much loan did Richard borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6720 to clear it?

(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.

(8) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.

(9) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.

(10) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.