Suppose you deposit $3,000 for 6 years at a rate of 7%. I don't understand this question.

Question

A=P(1+ r/n)^nt        All work needs to be shown on how answer was calculated

a) Calculate the return (A) if the bank compounds semi-annually. Round your answer to the nearest cent.

b) Calculate the return (A) if the bank compounds monthly. Round your answer to the nearest cent.

c) If a bank compounds continuously, then the formula used is where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the nearest cent.

Answer 1

This is a compound interest formula, where P = principal, r = rate, n = # compoundings per yr, t = time (in years).

P = 3000
r = 7% = 0.07
t = 6
n = 2 (semi-annually)

a) A = 3000(1 + 0.07/2)^(2*6) = $4,533.21

b) A = 3000(1 + 0.07/12)^(12*6) = $4,560.32 

Continuous compounding: A = Pe^(rt)

c) A = 3000(2.7183)^(0.07*6) = $4,565.90

Answer 2

Compound interest formula:     A = P(1 + r/n)^nt   , where

     A = amount of money accumulated after an x number of years

     P = principal amount (initial amount deposited/borrowed)

     r = annual rate of interest (in decimal form)

     t = number of years amount is deposited/borrowed

     n = number of times the interest is compounded per year

The first part (a) states that the bank is compounding the interest on the deposit semi-annually. Since semi means half, this means that the interest is being compounded two times per year. Therefore, given the following:   P = $3000 ,   r = 7%/100% = 0.07 ,   t = 6 ,   n = 2 ,   we can calculate A

     A = 3000(1 + 0.07/2)^2·6 = 3000(1 + 0.035)¹²

        = 3000(1.035)¹² = 4533.2059

     A ≈ $4,533.21

The second part (b) says that the interest is being compounded monthly, which means that the interest is being compounded 12 times per year since there are 12 months in a year. So, we use the same equation and given info as above but this time   n = 12.

     A = 3000(1 + 0.07/12)^12·6 = 3000(1 + 0.0058333333)⁷²

        = 3000(1.0058333333)⁷² = 4560.3165

     A ≈ $4,560.32

The last part of the problem (c) states that the interest is being compounded continuously, which uses a slightly different formula. The continuous compound interest formula is as follows:

     A = Pe^rt ,   where e is a constant the equals approximately 2.7183

Therefore,

     A = 3000e^0.07·6 = 3000e^0.42 = 3000(2.7183)^0.42 = 4565.897

     A ≈ $4,565.90