Simple Interest
Math MCQs

Question :    How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?

Correct Answer  $6100

Solution & Explanation

Solution

Given,

Amount (A) = $7625

Rate of Simple Interest (R) = 5%

Time (T) = 5 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

$7625 = P (1 + 5% × 5)

⇒ $7625 = P (1 + ⁵/₁₀₀ × 5)

⇒ $7625 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $7625 = P (1 + ²⁵/₁₀₀)

⇒ $7625 = P (^{100 + 25}/₁₀₀)

⇒ $7625 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $7625

⇒ P = ⁷⁶²⁵/_¹²⁵/100

⇒ P = 7625 × ¹⁰⁰/₁₂₅

⇒ P = ^{7625 × 100}/₁₂₅

⇒ P = ⁷⁶²⁵⁰⁰/₁₂₅

⇒ P = $6100

Thus, the sum borrowed (P) = $6100 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 = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 7625, then the Principal = ¹⁰⁰/₁₂₅ × 7625

= ^{100 × 7625}/₁₂₅

= ⁷⁶²⁵⁰⁰/₁₂₅

= 6100

Thus, Principal = $6100

Thus, the sum borrowed = $6100 Answer

Similar Questions

(1) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(2) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.

(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.

(4) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.

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

(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

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

(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.

(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 3 years.

(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.