Juanita and Sam attend a beach party and notice that the local beach appears to have a great deal more trash washed up on shore
1 answer:
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Answer:
1. Interest compounded annually = $18,049.74
2. Interest compounded quarterly = $18,493.77
3. Interest compounded Monthly = $18,598.16
4. Interest compounded continuously = $18,651.19
Explanation:
First let me state the formula for compound interest:
The future value of a certain amount which is compounded is the total amount (Principal + interest) on the amount of money, after compound interests have been applied, and this is shown below:
FV = PV
where:
FV = Future value
PV = Present value = $7,000
r = interest rate in decimal = 0.07
n = number of compounding periods per year
t = compounding period in years = 14
For interests compounded continuously, the Future value is given as:
FV = PV ×
where
is a mathematical constant which is = 2.7183
Now to calculate each on the compounding periods one after the other:
1. Interest compounded annually:
here n (number of compounding periods annually) = 1
Therefore,
FV = 7,000 ×
FV = 7,000 × = $18,049.74
2. Interest compounded quarterly:
here, n = 3 ( there are 4 quarters in a year)
FV = 7,000 ×
FV = 7,000 × = $18,493.77
3. Interest compounded Monthly:
here n = 12 ( 12 months in a year)
FV = 7,000 ×
FV = 7,000 × = $18,598.16
4. Interests compounded continuously:
FV = PV ×
FV = 7,000 × 2.66446 = $18,651.19
Answer:
b. 1,062.81
Explanation:
the key to answer this question is to remember that valuation of a bond depends basically of calculating the present value of a series of cash flows, so let´s think about a bond as if you were a lender so you will get interest by the money you lend (coupon) and at the end of n years you will get back the money you lend at the beginnin (principal), so applying math we have the bond value given by:
where: principal as said before is the value lended, coupon is the rate of interest paid, i is the interest rate and n is the number of periods
so applying to this particular exercise, as it is not said we will assume that 6% and 7% are interest rate convertible seminually, so the price of the bond will be:
price=1,062.81
take into account that here we are asked about semianually payments, so in 8 years there are 16 semesters.