Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 6% 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  9

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 6% 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 × 6}

= ³²⁹⁴⁰⁰/₃₆₆₀₀

= 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) = $6100

Rate of Simple Interest (R) = 6% 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 = 6% of Principal

= 6% of $6100

= ⁶/₁₀₀ × 6100

= ^{6 × 6100}/₁₀₀

= ³⁶⁶⁰⁰/₁₀₀ = 366

Thus, simple Interest for 1 year = $366

Now,

∵ If the simple Interest is $366, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₃₆₆ years

∴ If the simple Interest is $3294, then the time = ¹/₃₆₆ × 3294 years

= ^{1 × 3294}/₃₆₆ years

= ³²⁹⁴/₃₆₆ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.

(2) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.

(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 8% simple interest?

(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?

(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 4% simple interest?

(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.

(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?

(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.

(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 2% simple interest?

(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?