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) How much loan did Ryan borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9480 to clear it?

(2) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.

(4) How much loan did Christopher borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6900 to clear it?

(5) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(6) How much loan did Susan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6497.5 to clear it?

(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?

(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 8 years.

(9) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6258 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.