On what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum be equal to ₹ 63? Mới nhất

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Nội dung chính

On what sum of money does the difference between the simple interest and compound interest in 2 years 5 % is ₹ 15

Solution

Let the sum of money =xSimple interest in
2 years
=P×R×T100where
P= Principal =x, Rate,
R=5% and Time,
T=2 yearsso Simple Interest
=x×5×2100=0.1xCompound interest:Amount after 1 year
=x+5% of
x=1.05xAmount after 2 years
=1.05x+5%(1.05x)=1.05x+0.0525x=1.1025xSo compound interest after
2 years
=1.1025x−x=0.1025xDifference of compound interest and simple interest
=0.1025x−0.1x=0.0025xThis difference in interest is given as
Rs.15. So
0.0025x=15⇒x=150.0025=Rs.6000Hence, the sum is Rs.
6000

Compound Interest: The future value (FV) of an investment of present value (PV) dollars earning interest an annual rate of r compounded m times per year for a period of t years is:

Nội dung chính

FV = PV(1 + r/m)mtor

FV = PV(1 + i)n

where i = r/m is the interest per compounding period and n
= mt is the number of compounding periods.

One may solve for the present value PV to obtain:

PV = FV/(1 + r/m)mt

Numerical Example: For 4-year investment of $20,000 earning 8.5% per year, with interest re-invested each month, the future value is

FV = PV(1 + r/m)mt = 20,000(1 + 0.085/12)(12)(4) = $28,065.30

Notice that the interest earned is $28,065.30 – $20,000 = $8,065.30 — considerably more than the corresponding simple interest.

Effective
Interest Rate: If money is invested an annual rate r, compounded m times per year, the effective interest rate is:

reff = (1 + r/m)m – 1.

This is the interest rate that would give the same yield if compounded only once per year. In this context r is also called the nominal rate, and is often denoted as rnom.

Numerical Example: A CD paying 9.8% compounded monthly has a nominal rate of rnom = 0.098, and an effective rate of:

r eff =(1
+ rnom /m)m = (1 + 0.098/12)12 – 1 = 0.1025.

Thus, we get an effective interest rate of 10.25%, since the compounding makes the CD paying 9.8% compounded monthly really pay 10.25% interest over the course of the year.

Mortgage Payments Components: Let where P = principal, r = interest rate per period, n = number of periods, k = number of payments, R = monthly payment, and D = debt balance after K payments, then

R = P
� r / [1 – (1 + r)-n]

and

D = P � (1 + r)k – R � [(1 + r)k – 1)/r]

Accelerating Mortgage Payments Components: Suppose one decides to pay more than the monthly payment, the question is how many months will it take until the mortgage is paid off? The answer is, the rounded-up, where:

n = log[x / (x � P � r)] / log (1 + r)

where Log is the logarithm in any base, say 10, or e.

Future Value
(FV) of an Annuity Components: Ler where R = payment, r = rate of interest, and n = number of payments, then

FV = [ R(1 + r)n – 1 ] / r

Future Value for an Increasing Annuity: It is an increasing annuity is an investment that is earning interest, and into which regular payments of a fixed amount are made. Suppose one makes a payment of R the end of each compounding period into an investment with a present value of PV, paying interest an
annual rate of r compounded m times per year, then the future value after t years will be

FV = PV(1 + i)n + [ R ( (1 + i)n – 1 ) ] / i where i = r/m is the interest paid each period and n = m � t is the total number of periods.

Numerical Example: You deposit $100 per month into an account that now contains $5,000 and earns 5% interest per year compounded monthly. After 10 years, the amount of money in the account is:

FV = PV(1 + i)n + [ R(1 + i)n – 1 ] /
i =
5,000(1+0.05/12)120 + [100(1+0.05/12)120 – 1 ] / (0.05/12) = $23,763.28

Value of a Bond:

V is the sum of the value of the dividends and the final payment.

You may like to perform some sensitivity analysis for the “what-if” scenarios by entering different numerical value(s), to make your “good” strategic decision.

Replace the existing numerical example, with your own case-information, and then click one the Calculate.

On what sum of money will the difference between simple interest and compound interest for 2 years 5% per annum be equal to Rs. 63/-

Rs. 24600/-Rs. 24800/-Rs. 25200/-Rs. 25500/-

Answer (Detailed Solution Below)

Option 3 : Rs. 25200/-

Free

Territorial Army Paper I – Full Mock Test

100 Questions 100 Marks 120 Mins

Given:

Time is 2 years

Rate is 5% per annum

The difference between simple interest and compound interest is Rs. 63.

Concept:

S.I = (P × R × T)/100

C.I = P[(1 + r/100)n – 1]

Here, n is the number of terms in the year

Calculation:

Let sum be Rs. P

Now,

The simple interest for 2 years 5% per annum is

(P × 5 × 2)/100

⇒ P/10

Now,

The compound interest for 2 years 5% per annum is

P[(1 + 5/100)2 – 1]

⇒ P[(21/20)2 – 1]

⇒ P[(441/400) – 1]

⇒ 41P/400

So,

The difference between Compound interest and simple interest is

⇒ 41p/400 – P/10 = 63

⇒ 41P – 40P = 63 ×
400

⇒ P = Rs. 25200

∴ The required sum of money is Rs. 25200.

Shortcut Trick

The difference between compound interest and simple interest for 2 years is

⇒ P(r/100)2

According to
question

⇒ P(5/100)2 = 63

⇒ P × 1/400 = 63

⇒ P = 63 × 400

⇒ P = 25200

∴ The required sum of money is Rs. 25200

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Last updated on Sep 22, 2022

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On what sum of money will the simple interest and compound interest for 2 years 5% per annum be equal to Rs 63?

The difference between simple interest and compound interest is Rs. 63. ∴ The required sum of money is Rs. 25200.

On what sum
will the compound interest 5% per annum for 2 years compounded annually be Rs 1647?

On what sum will the compound interest 5% per annum for 2 years compounded annually be ₹164. The required sum is ₹1600.

On what sum of money will the simple interest and compound interest for 2 years 5% per annum be equal to Rs 25?

Hence, the required
answer is Rs. 20,000.

On what sum of money will the interest 5% pa for 4 years be the same as that on 2500 3% pa for 6 years?

Answer. Answer: 2250 rs. P = 2250 rs.

On what sum of money will the difference between simple interest and compound interest for 2 years 5% per annum?

Hence, the sum is Rs. 6000.

On what sum of money will the difference between simple interest and compound interest for 2 years 5% per annum is rupees 12 find the sum of money?

This is Expert Verified Answer
And based on a two-year compounded interest rate and the rate of %. Hence, the required answer is Rs. 20,000.

What is the formula of difference between simple interest and compound interest for 2 years?

We will discuss here how to find the difference of compound interest and simple interest. If the rate of interest per annum is the same under both simple interest and compound interest then for 2 years, compound interest (CI) – simple interest (SI) = Simple interest for 1 year on “Simple interest for one year”.

On what sum of money will the difference between the simple interest and compound interest for 3 years be equal to Rs 930 if the rate of interest charged for both is 10?

This is Expert Verified Answer
Difference between the compound interest and simple interest for 3 years be equal to 930, if the rate of interest charged for both is 10% p..a. To Find: What is sum of money? Means amount of sum is 30000 Rupees.
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