Simple Interest
Math MCQs

Question :    Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6900

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

Amount (A) = $9798

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 = $9798 – $6900 = $2898

Thus, Simple Interest = $2898

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 × 2898}/_{6900 × 7}

= ²⁸⁹⁸⁰⁰/₄₈₃₀₀

= 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) = $6900

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

Simple Interest = $2898 (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 $6900

= ⁷/₁₀₀ × 6900

= ^{7 × 6900}/₁₀₀

= ⁴⁸³⁰⁰/₁₀₀ = 483

Thus, simple Interest for 1 year = $483

Now,

∵ If the simple Interest is $483, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₈₃ years

∴ If the simple Interest is $2898, then the time = ¹/₄₈₃ × 2898 years

= ^{1 × 2898}/₄₈₃ years

= ²⁸⁹⁸/₄₈₃ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.

(2) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.

(3) If Elizabeth paid $4002 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(4) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.

(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.

(7) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?

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

(9) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $11560 to clear the loan, then find the time period of the loan.

(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.