Simple Interest
Math MCQs

Question :    Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 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) = 7% per annum

Amount (A) = $8662

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 = $8662 – $6100 = $2562

Thus, Simple Interest = $2562

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 × 2562}/_{6100 × 7}

= ²⁵⁶²⁰⁰/₄₂₇₀₀

= 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) = 7% per annum

Simple Interest = $2562 (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 = 7% of Principal

= 7% of $6100

= ⁷/₁₀₀ × 6100

= ^{7 × 6100}/₁₀₀

= ⁴²⁷⁰⁰/₁₀₀ = 427

Thus, simple Interest for 1 year = $427

Now,

∵ If the simple Interest is $427, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₇ years

∴ If the simple Interest is $2562, then the time = ¹/₄₂₇ × 2562 years

= ^{1 × 2562}/₄₂₇ years

= ²⁵⁶²/₄₂₇ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?

(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?

(3) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.

(4) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 3% simple interest?

(5) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?

(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.

(7) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.

(8) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.

(9) If Susan borrowed $3650 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.

(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?