Simple Interest
Math MCQs

Question :    If Jennifer paid $3900 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.

Correct Answer  $3250

Solution & Explanation

Solution

Given,

Amount (A) = $3900

Rate of Simple Interest (R) = 5%

Time (T) = 4 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

$3900 = P (1 + 5% × 4)

⇒ $3900 = P (1 + ⁵/₁₀₀ × 4)

⇒ $3900 = P (1 + ^{5 × 4}/₁₀₀)

⇒ $3900 = P (1 + ²⁰/₁₀₀)

⇒ $3900 = P (^{100 + 20}/₁₀₀)

⇒ $3900 = P × ¹²⁰/₁₀₀

⇒ P × ¹²⁰/₁₀₀ = $3900

⇒ P = ³⁹⁰⁰/_¹²⁰/100

⇒ P = 3900 × ¹⁰⁰/₁₂₀

⇒ P = ^{3900 × 100}/₁₂₀

⇒ P = ³⁹⁰⁰⁰⁰/₁₂₀

⇒ P = $3250

Thus, the sum borrowed (P) = $3250 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 = 4 years

So, we need to calculate the simple interest for the given time period, which is 4 years

Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year

= 4 × 5 = 20

Thus, simple interest for 4 years = 20

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 20 = 120

Calculation of the Principal

Now,

∵ If the Amount is 120, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₀

∴ If the Amount is 3900, then the Principal = ¹⁰⁰/₁₂₀ × 3900

= ^{100 × 3900}/₁₂₀

= ³⁹⁰⁰⁰⁰/₁₂₀

= 3250

Thus, Principal = $3250

Thus, the sum borrowed = $3250 Answer

Similar Questions

(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?

(2) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?

(3) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(4) How much loan did Timothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8140 to clear it?

(5) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.

(6) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.

(8) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $9238 to clear the loan, then find the time period of the loan.

(9) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?

(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 5% simple interest?