Simple Interest
Math MCQs

Question :    If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

Correct Answer  $4100

Solution & Explanation

Solution

Given,

Amount (A) = $4756

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

$4756 = P (1 + 4% × 4)

⇒ $4756 = P (1 + ⁴/₁₀₀ × 4)

⇒ $4756 = P (1 + ^{4 × 4}/₁₀₀)

⇒ $4756 = P (1 + ¹⁶/₁₀₀)

⇒ $4756 = P (^{100 + 16}/₁₀₀)

⇒ $4756 = P × ¹¹⁶/₁₀₀

⇒ P × ¹¹⁶/₁₀₀ = $4756

⇒ P = ⁴⁷⁵⁶/_¹¹⁶/100

⇒ P = 4756 × ¹⁰⁰/₁₁₆

⇒ P = ^{4756 × 100}/₁₁₆

⇒ P = ⁴⁷⁵⁶⁰⁰/₁₁₆

⇒ P = $4100

Thus, the sum borrowed (P) = $4100 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 4756, then the Principal = ¹⁰⁰/₁₁₆ × 4756

= ^{100 × 4756}/₁₁₆

= ⁴⁷⁵⁶⁰⁰/₁₁₆

= 4100

Thus, Principal = $4100

Thus, the sum borrowed = $4100 Answer

Similar Questions

(1) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 8 years.

(2) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 8% simple interest.

(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.

(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?

(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 9% simple interest?

(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.

(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 4 years.

(9) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 8% simple interest?

(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.