A initial investment of $10,000 grows at per year. What function tells value of the investment after t years?

Answer 1

First, let us be clear on the question. Let us assume that the interest rate is r per year and is paid n times per year. If the interest rate is 8% per year, that means r = 0.08. If it is 10% per year, r = 0.10 and so on. If the interest is paid monthly, then n = 12 because it will be paid twelve times a year. If the interest is paid quarterly, it will be paid 4 times per year, so n = 4.

Let us let P be the principal, which is the amount on which the interest is computed. Let Po be the amount you start off with, in this example, that would be ten thousand dollars, so Po = 10000.

At the end of each pay period, you will get

i = Pr / n

back in interest.

The value of your investment depends on one other thing: what you do with the interest. Two common ways to treat this is to draw off the interest as income as it accumulates or to redeposit it along with the existing principal, adding to the amount you are investing.

If you draw off the interest as income, you leave the principal unchanged, so you will get n equal interest payments each year, each one being Po*r/n, for a total interest during the year of

i = Po * r

If you operate like this, you will therefore get a total of

i = Po * r * t

in interest payments, and you still have your original principal, for a total value of

Po + Po*r*t

The more interesting case occurs if you invest your interest along with the principal. In that case, you still get i = Po*r/n in interest, but after you reinvest your interest, your new principal will be

P = Po + Po*r/n or Po*(1 + r/n)

Furthermore, after each pay period, your principal will have increased by the same factor. After one year, you will have compounded your interest n times and your principal will be

P = Po*(1 + r/n)^n

with the total interest accrued being

i = Po * ( (1 + r/n)^n - 1)

The number (1 + r/n)^n - 1, when expressed as a percentage is what banks call annual percentage yield APY and is a little greater than r, the annual percentage rate, often abbreviated APR. Each year, the principal will be greater than it was the previous year by the factor 1 + APY. After t years, the value of the investment will then be

P = Po * (1 + APY)^t
= Po * (1 + r/n)^(n*t)

Although the value of the investment is only slightly bigger than it would be after the first few years, by the time the value of the simple interest investment doubled, the compound interest investment would have increased to about 2.7 times its initial value - and the bigger it gets, the faster it grows.

Answer 2

FV = 10,000(1+r)^y,
where r is the rate expressed as a decimal, y is the number of years, and FV is the Future Value.This for interest per year, that is, no compounding.

If interest were compouded monthly the formula would be:
FV= 10,000(1+r/12)^(12y)

Answer 3

You multiple the principle by 1 + the interest rate raised by the xth power where x is the number of years

Answer 4

make sure with the banks on your section to workout consultation who has the optimal fee for 6 month cds. i imagine you've gotten to have a ascertain open the account. once you're as plenty as $one thousand placed it in a money market Mutual Fund at top-rated side. sturdy fulfillment!

Answer 5

after t years it will be x

x=a+(t-1)*10000