Simple Interest
Math MCQs

Question :    Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6300

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10269

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $10269 – $6300 = $3969

Thus, Simple Interest = $3969

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 3969}/_{6300 × 7}

= ³⁹⁶⁹⁰⁰/₄₄₁₀₀

= 9 years (using formula)

Thus, Time (T) = 9 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $6300

Rate of Simple Interest (R) = 7% per annum

Simple Interest = $3969 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 7% of Principal

= 7% of $6300

= ⁷/₁₀₀ × 6300

= ^{7 × 6300}/₁₀₀

= ⁴⁴¹⁰⁰/₁₀₀ = 441

Thus, simple Interest for 1 year = $441

Now,

∵ If the simple Interest is $441, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₄₁ years

∴ If the simple Interest is $3969, then the time = ¹/₄₄₁ × 3969 years

= ^{1 × 3969}/₄₄₁ years

= ³⁹⁶⁹/₄₄₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?

(2) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.

(3) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(4) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 4 years.

(5) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.

(6) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $8320 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.

(8) Calculate the amount due if David borrowed a sum of $3400 at 3% simple interest for 3 years.

(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.