Simple Interest
Math MCQs

Question :    If Sarah paid $4466 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $3850

Solution & Explanation

Solution

Given,

Amount (A) = $4466

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

$4466 = P (1 + 4% × 4)

⇒ $4466 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4466 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4466 = P (1 + ¹⁶/₁₀₀)

⇒ $4466 = P (^{100 + 16}/₁₀₀)

⇒ $4466 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4466

⇒ P = ⁴⁴⁶⁶/_¹¹⁶/100

⇒ P = 4466 × ¹⁰⁰/₁₁₆

⇒ P = ^{4466 × 100}/₁₁₆

⇒ P = ⁴⁴⁶⁶⁰⁰/₁₁₆

⇒ P = $3850

Thus, the sum borrowed (P) = $3850 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 4466, then the Principal = ¹⁰⁰/₁₁₆ × 4466

= ^{100 × 4466}/₁₁₆

= ⁴⁴⁶⁶⁰⁰/₁₁₆

= 3850

Thus, Principal = $3850

Thus, the sum borrowed = $3850 Answer

Similar Questions

(1) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.

(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.

(3) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.

(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.

(5) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?

(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.

(7) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?

(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.

(9) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.