Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 8% per annum

Amount (A) = $7544

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 = $7544 – $4600 = $2944

Thus, Simple Interest = $2944

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 × 2944}/_{4600 × 8}

= ²⁹⁴⁴⁰⁰/₃₆₈₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $4600

Rate of Simple Interest (R) = 8% per annum

Simple Interest = $2944 (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 = 8% of Principal

= 8% of $4600

= ⁸/₁₀₀ × 4600

= ^{8 × 4600}/₁₀₀

= ³⁶⁸⁰⁰/₁₀₀ = 368

Thus, simple Interest for 1 year = $368

Now,

∵ If the simple Interest is $368, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₈ years

∴ If the simple Interest is $2944, then the time = ¹/₃₆₈ × 2944 years

= ^{1 × 2944}/₃₆₈ years

= ²⁹⁴⁴/₃₆₈ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $11520 to clear the loan, then find the time period of the loan.

(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.

(3) If Patricia paid $3528 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.

(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?

(5) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(6) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.

(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?

(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.

(9) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.

(10) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.