Suntali deposited Rs 9000 altogether in her saving account and fixed deposit account in a bank. saving account give her 5% p.a interest compounded annually and fixed deposit account gives 10% p.a. interest compounded half yearly. if she got Rs 160 more interest from fixed deposit account at the end of one year find how much money did she deposit in her each account? plz answer me fast
Answers
Step-by-step explanation:
Year 1 - You earn interest on your Principal.
Year 2 - You earn interest on your (Principal + Interest of Year 1).
Year 3 - You earn interest on your (Principal + Interest of Year 1 + Interest of Year 2).
Compound interest is the basis of long-term growth of the stock market. It forms the basis of personal savings plans. Compound interest also affects inflation.
Types of Compound Interest
There are generally two types of compound interest used.
Periodic Compounding - Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.
Continuous Compounding - This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equalled to the constant rate of growth for all natural growth. This figure was born out of physics. It uses Euler’s number which is a famous irrational number which is known to more than 1 trillion digits of accuracy. Euler’s number is denominated by the letter “E”.
Periodic Compound Interest Formula Overview
There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:
The total value of the deposit.
The total compound interest earned.
Value of the Deposit
Formulas can be a deterrent to many. If you aren’t savvy with math, your eyes turn away from these codes or just skip them altogether. But once it’s explained, it’s pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:
P (1+ i/n)nt
P = Principal invested.
i = Nominal Rate of Interest.
n = Compounding Frequency or number of compounding periods in a year.
t = Time, meaning the length of time the interest is applicable, generally in years.
Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied to the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.
Total Compound Interest Earned
To find out how much interest was earned, you can use the following formula for Compound Interest.
P[(1+ i/n))nt-1]
Compound Interest Equation and Calculation
To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.
Period Deposit Balance
Investment P
Year 1 P + iP
Year 2 (P+ iP) + i(P+iP)
To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:
Period Deposit Balance
Answer:
Deposited money (p)1 = Rs 5,000
Fixed deposited money(p) 2 = Rs. 4000
Step-by-step explanation:
let the money deposited (p)1 = x
time (T) = 1year
R = 5%
compound interest (c.i)= ?
we know,
For deposited money
c.i = p[(1 +R\100) ^T -1]
= x[(1 +5\100) ^1-1]
= x[1.05-1]
=0.05x
Again,
For fixed deposited money
nd
fixed money deposited (p)2=9000-x
time (T) =2
Rate (R) = 10%
Half-early compound interest (c.i)= ?
we know,,
Half-early (c.i)= p[(1 +R\200) ^2T -1]
= 9000-x [(1 +10\200) ^2×1 -1]
=9000-x [(1.05) ^2-1]
=9000 - x[ 1.1025-1]
= 9000-x(0.1025)
=9,922.5 x 0.1025 - 0.1025x
=922.5- 0.1025x
According to the question
half yearly c. - yearly c. i= Rs. 160
(922.5 -0. 1025x ) - 0.05x = 160
922.5 - 160 = 0.1525x
x = 762.5\ 0.1525
x = Rs. 5,000
So, the money deposited (p)1 =Rs5,000
fixed money deposited (p)2=9000-5000
= Rs 4,000