Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $7332

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 = $7332 – $4700 = $2632

Thus, Simple Interest = $2632

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 × 2632}/_{4700 × 8}

= ²⁶³²⁰⁰/₃₇₆₀₀

= 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) = $4700

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

Simple Interest = $2632 (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 $4700

= ⁸/₁₀₀ × 4700

= ^{8 × 4700}/₁₀₀

= ³⁷⁶⁰⁰/₁₀₀ = 376

Thus, simple Interest for 1 year = $376

Now,

∵ If the simple Interest is $376, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₇₆ years

∴ If the simple Interest is $2632, then the time = ¹/₃₇₆ × 2632 years

= ^{1 × 2632}/₃₇₆ years

= ²⁶³²/₃₇₆ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?

(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7912 to clear the loan, then find the time period of the loan.

(4) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?

(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?

(6) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.

(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.

(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.

(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.