Simple Interest
Math MCQs

Question :    Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5800

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

Amount (A) = $8932

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 = $8932 – $5800 = $3132

Thus, Simple Interest = $3132

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 × 3132}/_{5800 × 9}

= ³¹³²⁰⁰/₅₂₂₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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) = $5800

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

Simple Interest = $3132 (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 $5800

= ⁹/₁₀₀ × 5800

= ^{9 × 5800}/₁₀₀

= ⁵²²⁰⁰/₁₀₀ = 522

Thus, simple Interest for 1 year = $522

Now,

∵ If the simple Interest is $522, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₂₂ years

∴ If the simple Interest is $3132, then the time = ¹/₅₂₂ × 3132 years

= ^{1 × 3132}/₅₂₂ years

= ³¹³²/₅₂₂ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 8% simple interest.

(2) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 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 $9540 to clear the loan, then find the time period of the loan.

(4) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?

(5) How much loan did Ashley borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7860 to clear it?

(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 7 years.

(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.

(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 4% simple interest for 8 years.

(10) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 3% simple interest for 7 years.