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) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.

(3) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?

(4) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?

(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?

(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 10% simple interest?

(7) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?

(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.

(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.

(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.