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 $9394 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $6100

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

Amount (A) = $9394

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 = $9394 – $6100 = $3294

Thus, Simple Interest = $3294

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 × 3294}/_{6100 × 9}

= ³²⁹⁴⁰⁰/₅₄₉₀₀

= 6 years (using formula)

Thus, Time (T) = 6 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 = $3294 (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 $3294, then the time = ¹/₅₄₉ × 3294 years

= ^{1 × 3294}/₅₄₉ years

= ³²⁹⁴/₅₄₉ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.

(3) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 4% simple interest?

(4) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.

(5) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.

(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.

(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.

(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.

(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.

(10) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.