Simple Interest
Math MCQs

Question :    Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.

Correct Answer  9

Solution & Explanation

Solution

Given,

Principal (P) = $5900

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

Amount (A) = $11210

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 = $11210 – $5900 = $5310

Thus, Simple Interest = $5310

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 × 5310}/_{5900 × 10}

= ⁵³¹⁰⁰⁰/₅₉₀₀₀

= 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) = $5900

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

Simple Interest = $5310 (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 $5900

= ¹⁰/₁₀₀ × 5900

= ^{10 × 5900}/₁₀₀

= ⁵⁹⁰⁰⁰/₁₀₀ = 590

Thus, simple Interest for 1 year = $590

Now,

∵ If the simple Interest is $590, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₉₀ years

∴ If the simple Interest is $5310, then the time = ¹/₅₉₀ × 5310 years

= ^{1 × 5310}/₅₉₀ years

= ⁵³¹⁰/₅₉₀ = 9 years

Thus, time (T) = 9 years Answer

Similar Questions

(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?

(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 3% simple interest?

(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.

(4) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.

(5) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?

(6) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?

(7) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?

(8) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.

(9) Donald had to pay $4905 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.

(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.