Simple Interest
Math MCQs

Question :    Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.

Correct Answer  6

Solution & Explanation

Solution

Given,

Principal (P) = $7000

Rate of Simple Interest (R) = 10% per annum

Amount (A) = $11200

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 = $11200 – $7000 = $4200

Thus, Simple Interest = $4200

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 × 4200}/_{7000 × 10}

= ⁴²⁰⁰⁰⁰/₇₀₀₀₀

= 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) = $7000

Rate of Simple Interest (R) = 10% per annum

Simple Interest = $4200 (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 = 10% of Principal

= 10% of $7000

= ¹⁰/₁₀₀ × 7000

= ^{10 × 7000}/₁₀₀

= ⁷⁰⁰⁰⁰/₁₀₀ = 700

Thus, simple Interest for 1 year = $700

Now,

∵ If the simple Interest is $700, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₇₀₀ years

∴ If the simple Interest is $4200, then the time = ¹/₇₀₀ × 4200 years

= ^{1 × 4200}/₇₀₀ years

= ⁴²⁰⁰/₇₀₀ = 6 years

Thus, time (T) = 6 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.

(2) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.

(3) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.

(4) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?

(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?

(6) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?

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

(8) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.

(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 4% simple interest?

(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.