Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $12489 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $6900

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $12489

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 = $12489 – $6900 = $5589

Thus, Simple Interest = $5589

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 × 5589}/_{6900 × 9}

= ⁵⁵⁸⁹⁰⁰/₆₂₁₀₀

= 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) = $6900

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $5589 (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 = 9% of Principal

= 9% of $6900

= ⁹/₁₀₀ × 6900

= ^{9 × 6900}/₁₀₀

= ⁶²¹⁰⁰/₁₀₀ = 621

Thus, simple Interest for 1 year = $621

Now,

∵ If the simple Interest is $621, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₆₂₁ years

∴ If the simple Interest is $5589, then the time = ¹/₆₂₁ × 5589 years

= ^{1 × 5589}/₆₂₁ years

= ⁵⁵⁸⁹/₆₂₁ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?

(2) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.

(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?

(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.

(5) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?

(6) Calculate the amount due if William borrowed a sum of $3500 at 3% simple interest for 4 years.

(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.

(9) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.

(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.