Simple Interest
Math MCQs

Question :    Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $5700

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

Amount (A) = $10260

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 = $10260 – $5700 = $4560

Thus, Simple Interest = $4560

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 × 4560}/_{5700 × 10}

= ⁴⁵⁶⁰⁰⁰/₅₇₀₀₀

= 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) = $5700

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

Simple Interest = $4560 (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 $5700

= ¹⁰/₁₀₀ × 5700

= ^{10 × 5700}/₁₀₀

= ⁵⁷⁰⁰⁰/₁₀₀ = 570

Thus, simple Interest for 1 year = $570

Now,

∵ If the simple Interest is $570, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₅₇₀ years

∴ If the simple Interest is $4560, then the time = ¹/₅₇₀ × 4560 years

= ^{1 × 4560}/₅₇₀ years

= ⁴⁵⁶⁰/₅₇₀ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.

(2) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.

(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 6% simple interest?

(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.

(5) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.

(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.

(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.

(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.

(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?

(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.