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 $10370 to clear the loan, then find the time period of the loan.

Correct Answer  10

Solution & Explanation

Solution

Given,

Principal (P) = $6100

Rate of Simple Interest (R) = 7% per annum

Amount (A) = $10370

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 = $10370 – $6100 = $4270

Thus, Simple Interest = $4270

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 × 4270}/_{6100 × 7}

= ⁴²⁷⁰⁰⁰/₄₂₇₀₀

= 10 years (using formula)

Thus, Time (T) = 10 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 = $4270 (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 $4270, then the time = ¹/₄₂₇ × 4270 years

= ^{1 × 4270}/₄₂₇ years

= ⁴²⁷⁰/₄₂₇ = 10 years

Thus, time (T) = 10 years Answer

Similar Questions

(1) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 4% simple interest?

(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?

(3) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?

(4) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11696 to clear the loan, then find the time period of the loan.

(5) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.

(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.

(7) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 2% simple interest?

(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 5% simple interest?

(9) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.

(10) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.