Simple Interest
Math MCQs

Question :    Barbara had to pay $4082.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

Correct Answer  $3550

Solution & Explanation

Solution

Given,

Amount (A) = $4082.5

Rate of Simple Interest (R) = 5%

Time (T) = 3 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

$4082.5 = P (1 + 5% × 3)

⇒ $4082.5 = P (1 + ⁵/₁₀₀ × 3)

⇒ $4082.5 = P (1 + ^{5 × 3}/₁₀₀)

⇒ $4082.5 = P (1 + ¹⁵/₁₀₀)

⇒ $4082.5 = P (^{100 + 15}/₁₀₀)

⇒ $4082.5 = P × ¹¹⁵/₁₀₀

⇒ P × ¹¹⁵/₁₀₀ = $4082.5

⇒ P = ^4082.5/_¹¹⁵/100

⇒ P = 4082.5 × ¹⁰⁰/₁₁₅

⇒ P = ^{4082.5 × 100}/₁₁₅

⇒ P = ⁴⁰⁸²⁵⁰/₁₁₅

⇒ P = $3550

Thus, the sum borrowed (P) = $3550 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 = 3 years

So, we need to calculate the simple interest for the given time period, which is 3 years

Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year

= 3 × 5 = 15

Thus, simple interest for 3 years = 15

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 15 = 115

Calculation of the Principal

Now,

∵ If the Amount is 115, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₁₅

∴ If the Amount is 4082.5, then the Principal = ¹⁰⁰/₁₁₅ × 4082.5

= ^{100 × 4082.5}/₁₁₅

= ⁴⁰⁸²⁵⁰/₁₁₅

= 3550

Thus, Principal = $3550

Thus, the sum borrowed = $3550 Answer

Similar Questions

(1) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.

(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 2% simple interest?

(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 8 years.

(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?

(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.

(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.

(7) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.

(8) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.

(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 7 years.

(10) In how much time a principal of $3000 will amount to $3180 at a simple interest of 2% per annum?