Final answer:
a. The future value (FV) of $1,000 invested at 10% interest after 6 years is $1,771.56.
b. The FV at rates of 0%, 5%, and 20% after 0-5 years are as follows: 0%: $1,000, 5%: $1,340.10, $1,407.10, $1,477.10, $1,550.96, $1,628.89, $1,711.06, 20%: $1,200, $1,440, $1,728, $2,073.60, $2,488.32, $2,985.98.
c. The present value (PV) of $1,000 due in 6 years with a 10% discount rate is $558.39.
d. The security provides a rate of return of 200%.
e. It will take approximately 18 years for California's population to double.
f. The PV of an ordinary annuity that pays $1,000 each year for 6 years at a 14% interest rate is $4,117.13, and the FV is $8,616.71.
Step-by-step explanation:
a. Find the FV of $1,000 invested to earn 10% after 6 years.
To find the future value (FV) of $1,000 invested to earn 10% after 6 years, we can use the formula:
FV = PV * (1 + r)^n
FV = $1,000 * (1 + 0.10)^6 = $1,771.56 (rounded to the nearest cent).
b. What is the investment's FV at rates of 0%, 5%, and 20% after 0, 1, 2, 3, 4, and 5 years?
To find the future value (FV) at different rates and time periods, we can use the same formula. Here are the rounded FV values:
At 0%: $1,000
At 5%: $1,340.10, $1,407.10, $1,477.10, $1,550.96, $1,628.89, $1,711.06
At 20%: $1,200, $1,440, $1,728, $2,073.60, $2,488.32, $2,985.98
c. Find the PV of $1,000 due in 6 years if the discount rate is 10%.
To find the present value (PV) of $1,000 due in 6 years with a discount rate of 10%, we can use the formula:
PV = FV / (1 + r)^n
PV = $1,000 / (1 + 0.10)^6 = $558.39 (rounded to the nearest cent).
d. What rate of return does the security provide?
The rate of return can be calculated using the formula:
ROR = (FV - Cost) / Cost * 100
ROR = ($3,000 - $1,000) / $1,000 * 100 = 200% (rounded to two decimal places).
e. How long will it take for California's population to double?
We can use the compound interest formula to calculate the time it takes for California's population to double:
Population = Initial Population * (1 + Growth Rate)^Time
35.4 million * (1 + 0.04)^Time = 70.8 million
(1.04)^Time = 2
Using logarithms, we can solve for Time: Time = log(2) / log(1.04) = 17.67 (rounded to the nearest whole number). Therefore, it will take approximately 18 years for California's population to double.
f. Find the PV and FV of an ordinary annuity that pays $1,000 each year for 6 years at an interest rate of 14%.
To find the present value (PV) of an ordinary annuity, we can use the formula:
PV = Payment * ((1 - (1 + r)^-n) / r)
PV = $1,000 * ((1 - (1 + 0.14)^-6) / 0.14) = $4,117.13 (rounded to the nearest cent).
To find the future value (FV) of an ordinary annuity, we can use the formula:
FV = Payment * ((1 + r)^n - 1) / r
FV = $1,000 * ((1 + 0.14)^6 - 1) / 0.14 = $8,616.71 (rounded to the nearest cent).
9. What effective annual rate does each bank pay and how much will you have in each bank after 1 and 2 years?
Unfortunately, the information about the banks and their interest rates is missing from the question. To answer this question accurately, we would need the specific interest rates offered by each bank.
10. What nominal rate will cause all of the banks to provide the same effective annual rate as Bank A?
We would need the effective annual rate for Bank A and the effective annual rates offered by the other banks to determine the nominal rate that would equalize the effective annual rates.
11. How large must the payments be for each bank if you need $6,000 at the end of 1 year?
To determine the payment needed for each bank, we need to know the interest rates offered by the banks and the payment frequency (annual, semiannual, quarterly, etc.). Without this information, it's not possible to calculate the payment size accurately.