Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.

Correct Answer  7

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 9% per annum

Amount (A) = $9943

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 = $9943 – $6100 = $3843

Thus, Simple Interest = $3843

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 × 3843}/_{6100 × 9}

= ³⁸⁴³⁰⁰/₅₄₉₀₀

= 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) = $6100

Rate of Simple Interest (R) = 9% per annum

Simple Interest = $3843 (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 = 9% of Principal

= 9% of $6100

= ⁹/₁₀₀ × 6100

= ^{9 × 6100}/₁₀₀

= ⁵⁴⁹⁰⁰/₁₀₀ = 549

Thus, simple Interest for 1 year = $549

Now,

∵ If the simple Interest is $549, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₄₉ years

∴ If the simple Interest is $3843, then the time = ¹/₅₄₉ × 3843 years

= ^{1 × 3843}/₅₄₉ years

= ³⁸⁴³/₅₄₉ = 7 years

Thus, time (T) = 7 years Answer

Similar Questions

(1) If Linda paid $3886 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.

(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.

(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8567.5 to clear it?

(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.

(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.

(7) Steven had to pay $4876 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.

(8) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?

(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

(10) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.