college algebra

Question

use the compound interest A=P(1+r/n)rt to solve the problem given round answer to the nearest cent. Find the accumulated value of an investment of 15,000 for 7 years at an interest rate 6.5% if the money is a compounded semiannually,quarterly, monthly, continuously round answer to the nearest cent

Answer 1

the underlying formula that you want to use here for compound interest is

A = P(1 + r/n)^(nt)

for this scenario that means taking

A = 15000(1 + 0.065/n)^(7n)

so you would just plug in the value of "n" based on the compound frequency that you are trying to measure ... annually means n = 1, quarterly means n = 4, monthly means n= 12, and so on

Answer 2

The correct formula is:

A = P (1 + r/n)^nt

1. A= value of investment at time t
2. P = initial investment = $15,000
3. r = rate expressed as a decimal = 6.5% = 0.065
4. n = number of compoundings per year = 2 for semiannual, 4 for quarterly, 12 for monthly
5. t = years = 7

Plug in the numbers and compute the answers on a calculator. For continuous compounding, the formula is:

A = Pe^rt

1. A= value of investment at time t
2. P = initial investment = $15,000
3. e = Euler's number (it's on your calculator)
4. r = rate expressed as a decimal = 6.5% = 0.065
5. t = years = 7

A = 15,000·e^0.065·7 = ____?

Again, use you calculator to compute the answer. For the same r and t, the more often an investment is compounded, the higher the return.