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) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 4% simple interest.

(2) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.

(4) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.

(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?

(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?

(7) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.

(8) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.

(9) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.

(10) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?