Simple Interest
Math MCQs

Question :    If Emily paid $5320 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

Correct Answer  $4750

Solution & Explanation

Solution

Given,

Amount (A) = $5320

Rate of Simple Interest (R) = 3%

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

$5320 = P (1 + 3% × 4)

⇒ $5320 = P (1 + ³/₁₀₀ × 4)

⇒ $5320 = P (1 + ^{3 × 4}/₁₀₀)

⇒ $5320 = P (1 + ¹²/₁₀₀)

⇒ $5320 = P (^{100 + 12}/₁₀₀)

⇒ $5320 = P × ¹¹²/₁₀₀

⇒ P × ¹¹²/₁₀₀ = $5320

⇒ P = ⁵³²⁰/_¹¹²/100

⇒ P = 5320 × ¹⁰⁰/₁₁₂

⇒ P = ^{5320 × 100}/₁₁₂

⇒ P = ⁵³²⁰⁰⁰/₁₁₂

⇒ 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 = 3% per annum

Thus, Interest = 3% of principal

⇒ Interest = 3% of 100 = 3

Thus, Simple Interest for 1 year = 3

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 × 3 = 12

Thus, simple interest for 4 years = 12

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 12 = 112

Calculation of the Principal

Now,

∵ If the Amount is 112, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₂

∴ If the Amount is 5320, then the Principal = ¹⁰⁰/₁₁₂ × 5320

= ^{100 × 5320}/₁₁₂

= ⁵³²⁰⁰⁰/₁₁₂

= 4750

Thus, Principal = $4750

Thus, the sum borrowed = $4750 Answer

Similar Questions

(1) How much loan did Daniel borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6710 to clear it?

(2) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.

(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.

(5) If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?

(7) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.

(8) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(9) How much loan did Andrew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7480 to clear it?

(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?