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 $8280 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $4600

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

Amount (A) = $8280

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 = $8280 – $4600 = $3680

Thus, Simple Interest = $3680

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 × 3680}/_{4600 × 8}

= ³⁶⁸⁰⁰⁰/₃₆₈₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $3680 (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 $3680, then the time = ¹/₃₆₈ × 3680 years

= ^{1 × 3680}/₃₆₈ years

= ³⁶⁸⁰/₃₆₈ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.

(2) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(3) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.

(4) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.

(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 7% simple interest.

(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 6% simple interest for 4 years.

(8) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.

(9) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.