Simple Interest
Math MCQs

Question :    Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4600

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6532

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 = $6532 – $4600 = $1932

Thus, Simple Interest = $1932

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 × 1932}/_{4600 × 6}

= ¹⁹³²⁰⁰/₂₇₆₀₀

= 7 years (using formula)

Thus, Time (T) = 7 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) = 6% per annum

Simple Interest = $1932 (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 = 6% of Principal

= 6% of $4600

= ⁶/₁₀₀ × 4600

= ^{6 × 4600}/₁₀₀

= ²⁷⁶⁰⁰/₁₀₀ = 276

Thus, simple Interest for 1 year = $276

Now,

∵ If the simple Interest is $276, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₇₆ years

∴ If the simple Interest is $1932, then the time = ¹/₂₇₆ × 1932 years

= ^{1 × 1932}/₂₇₆ years

= ¹⁹³²/₂₇₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.

(2) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

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

(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.

(5) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.

(6) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.

(8) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.

(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.

(10) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.