Simple Interest
Math MCQs

Question :    How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?

Correct Answer  $8000

Solution & Explanation

Solution

Given,

Amount (A) = $10000

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

$10000 = P (1 + 5% × 5)

⇒ $10000 = P (1 + ⁵/₁₀₀ × 5)

⇒ $10000 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $10000 = P (1 + ²⁵/₁₀₀)

⇒ $10000 = P (^{100 + 25}/₁₀₀)

⇒ $10000 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $10000

⇒ P = ¹⁰⁰⁰⁰/_¹²⁵/100

⇒ P = 10000 × ¹⁰⁰/₁₂₅

⇒ P = ^{10000 × 100}/₁₂₅

⇒ P = ^1000000/₁₂₅

⇒ P = $8000

Thus, the sum borrowed (P) = $8000 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 10000, then the Principal = ¹⁰⁰/₁₂₅ × 10000

= ^{100 × 10000}/₁₂₅

= ^1000000/₁₂₅

= 8000

Thus, Principal = $8000

Thus, the sum borrowed = $8000 Answer

Similar Questions

(1) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?

(2) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(3) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.

(4) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13800 to clear the loan, then find the time period of the loan.

(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?

(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.

(7) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.

(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?

(9) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.

(10) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?