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 $8084 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $4700

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

Amount (A) = $8084

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 = $8084 – $4700 = $3384

Thus, Simple Interest = $3384

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 × 3384}/_{4700 × 8}

= ³³⁸⁴⁰⁰/₃₇₆₀₀

= 9 years (using formula)

Thus, Time (T) = 9 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 = $3384 (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 $3384, then the time = ¹/₃₇₆ × 3384 years

= ^{1 × 3384}/₃₇₆ years

= ³³⁸⁴/₃₇₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.

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

(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?

(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(5) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.

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

(8) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.

(9) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?

(10) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $9384 to clear the loan, then find the time period of the loan.