Simple Interest
Math MCQs

Question :    If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5510

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

$5510 = P (1 + 4% × 4)

⇒ $5510 = P (1 + ⁴/₁₀₀ × 4)

⇒ $5510 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $5510 = P (1 + ¹⁶/₁₀₀)

⇒ $5510 = P (^{100 + 16}/₁₀₀)

⇒ $5510 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $5510

⇒ P = ⁵⁵¹⁰/_¹¹⁶/100

⇒ P = 5510 × ¹⁰⁰/₁₁₆

⇒ P = ^{5510 × 100}/₁₁₆

⇒ P = ⁵⁵¹⁰⁰⁰/₁₁₆

⇒ P = $4750

Thus, the sum borrowed (P) = $4750 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 5510, then the Principal = ¹⁰⁰/₁₁₆ × 5510

= ^{100 × 5510}/₁₁₆

= ⁵⁵¹⁰⁰⁰/₁₁₆

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?

(2) Joshua had to pay $5488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.

(5) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?

(7) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.

(8) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.

(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?

(10) How much loan did Michael borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5830 to clear it?