Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $10360 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $10360

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 = $10360 – $7000 = $3360

Thus, Simple Interest = $3360

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 × 3360}/_{7000 × 6}

= ³³⁶⁰⁰⁰/₄₂₀₀₀

= 8 years (using formula)

Thus, Time (T) = 8 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) = $7000

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $3360 (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 $7000

= ⁶/₁₀₀ × 7000

= ^{6 × 7000}/₁₀₀

= ⁴²⁰⁰⁰/₁₀₀ = 420

Thus, simple Interest for 1 year = $420

Now,

∵ If the simple Interest is $420, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₄₂₀ years

∴ If the simple Interest is $3360, then the time = ¹/₄₂₀ × 3360 years

= ^{1 × 3360}/₄₂₀ years

= ³³⁶⁰/₄₂₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.

(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.

(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.

(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.

(5) 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.

(6) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.

(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.

(8) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 4% simple interest?

(9) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.

(10) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 4 years.