Simple Interest
Math MCQs

Question :    Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $5200

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

Amount (A) = $7384

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 = $7384 – $5200 = $2184

Thus, Simple Interest = $2184

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 × 2184}/_{5200 × 7}

= ²¹⁸⁴⁰⁰/₃₆₄₀₀

= 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) = $5200

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

Simple Interest = $2184 (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 $5200

= ⁷/₁₀₀ × 5200

= ^{7 × 5200}/₁₀₀

= ³⁶⁴⁰⁰/₁₀₀ = 364

Thus, simple Interest for 1 year = $364

Now,

∵ If the simple Interest is $364, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₄ years

∴ If the simple Interest is $2184, then the time = ¹/₃₆₄ × 2184 years

= ^{1 × 2184}/₃₆₄ years

= ²¹⁸⁴/₃₆₄ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?

(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7568 to clear the loan, then find the time period of the loan.

(3) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.

(4) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.

(5) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 5% simple interest?

(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 4% simple interest?

(7) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.

(8) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.

(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?

(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.