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) What amount does William have to pay after 5 years if he takes a loan of $3500 at 2% simple interest?

(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.

(3) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(4) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(5) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.

(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?

(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?

(9) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.