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) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?

(2) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.

(3) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.

(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.

(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.

(6) Michelle had to pay $5247 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.

(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.

(10) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?