Choi deposited $2500 in a savings account that pays 4.75% interest compounded quarterly. What will be the total amount of money in the account 15 years from the day of deposit?
what level math is this for?
Compound Interest
With compound interest, the interest due and paid at the end of the interest compounding period is added to the initial starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest.
In its most basic use, if P is an amount deposited into an account paying a periodic interest, then Sn is the final compounded amount accumulated where
.......Sn = P(1+i)^n
where i is the periodic interest rate in decimal form = %Int./(100m), n is the number of interest bearing periods, and m is the number of interest paying periods per year.
For example, the compound amount and the compound interest on $5000.00 resulting from the accumulation of interest at 6% annual interest compounded monthly for 10 years is as follows:
Since m = 12, i = .06/12 = .005. Since we are dealing with a total of 10 years with 12 interest periods per year, n = 10 x 12 = 120. From this we get
Sn = $5000(1+.005)^120 = $5000(1.8194) = $9097.
Consequently, the compound interest realized is $9097 - $5000 = $4097. Of course the compound interest rate can be calculated directly from the simple expression
......I = P[(1+i)^n - 1].
For your example, P = $2500, n = 15(4) = 60 and i = 4.75/4(100) = .011875.
To calculate the total amount of money in the account 15 years from the day of deposit, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = the total amount of money in the account after time t
P = the principal amount (initial deposit)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case:
P = $2500
r = 4.75% or 0.0475 (converted to decimal form)
n = 4 (interest compounded quarterly)
t = 15 years
Now, let's substitute these values into the formula and solve for A:
A = 2500(1 + 0.0475/4)^(4*15)
A = 2500(1 + 0.011875)^(60)
A = 2500(1.011875)^(60)
A ≈ 2500(1.8314)
A ≈ $4,578.50
Therefore, the total amount of money in the account 15 years from the day of deposit will be approximately $4,578.50.
To calculate the total amount of money in Choi's savings account after 15 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the total amount of money in the account after time t,
P is the principal amount (the initial deposit),
r is the interest rate,
n is the number of times interest is compounded per year, and
t is the number of years.
Given:
P = $2500 (Choi's initial deposit),
r = 4.75% (expressed as a decimal, so r = 0.0475),
n = 4 (quarterly compounding, so 4 times per year),
t = 15 years.
Now, let's plug the values into the formula:
A = $2500(1 + 0.0475/4)^(4*15)
= $2500(1 + 0.011875)^(60)
= $2500(1.011875)^(60)
≈ $5312.40
Therefore, the total amount of money in Choi's savings account after 15 years would be approximately $5312.40.