Variable Annuity Comparison

R is the rate of interest and n is the number of years. The n is an exponential value of 1+r. It can also be written as (r^-1)(1-(1+r)^n).
As written the formula for the Present value of annuity of $1 in Arrears; (1/r)(1-(1/(1+r)^n)). For each dollar invested per n years, the principal will grow by the ammount given. I am trying to solve for r. So it could be A=(P)(1/r)(1-(1/(1+r)^n)) where A is the Amount (or total), P is the Principal, r is the rate, and n is the number of years.

Payments of 2,500 made at the beginning of each semiannual period for 15 years at 10%

Answers
163,597.12
153,306.78
87,374.32
174,401.97

The higher the rate used in determining the future value of a $1 annuity,
a) the smaller the future value at the end of the period.
b) the greater the future value at the end of a period.
c) the greater the present value at the beginning of a period.
d) none of the above – the interest has no effect on the future value of an annuity

For example: $1000 contribution per month for first year at 12% p.a compounded monthly. Contributions increase by 7% each year i.e. second year contributions will be $1070.

What is the future value of a 5-year annuity due that promises to pay you $300 each year? Assume that all payments are reinvested at 7 percent a year, until Year 5.

The ordinary annuity pays $300.00 each year at a 7% interest rate.

find the present value to the nearest dollar on January 1 of an annuity which pays $2000 every six months for fiver years. The first payment is due on the next April 1 and the rate of interest is 9% convertible semiannually

I am not too sure how to work out the following question on present value of multiple amounts.

The formula given from a hint is:

Annuity factor(n periods, r %) of $1 =
Present value / annuity amount (see table)

Question:

A dealer offers you financing to purchase a car priced at $11,000. Under the financial plan, you would pay $2,500 now and $2,500 at the end of each year for 5 years.
The finance plan has an implied annual interest rate ( to the nearest percent) of ?

A) 8%
B) 6%
C) 4%
D) 14%

Since they want $2,500 now, it’s going to be something like this…

2,500 + 2,500 * Annuity factor ( annual interest, 4years)

That’s all I can figure out so far…
Could anyone please help me out on this with your working step by step? Or any hints would be appreciated.

Thank you very much.

Thank you.

A bond with a maturity value of $100,000 has a stated rate of 8%. The bond matures in 10 years. When the bond is issued, the market rate of interest is 10%. What amount should be reported when the bond is issued?

Answer: $87,707

I’m pretty sure you have to use some tables (present/future value of annuity/single sum), but I’m not sure which one. I tried them all and I didn’t get the answer. Anyone know?

What is the future value of a 5-year ordinary annuity that promises to pay you $300 each year? The rate of interest is 7 percent.

I really need help with this problem. I have been working for hours on it and cannot figure it out at all. Examples in math book do not help at all.

Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.)
$160 monthly payment, 6.5% interest, 13 years.
If you could provide me with the formulas and how to do it, that would be great! Thank you so much.

I need help on this problem: Summit Co. issued 1,000,000, 10-year bonds and agreed to make annual sinking fund deposits of $80,000. The deposits are made at the end of each year into an account paying 5% annual interest. What amount will be in the sinking fund at the end of 10 years?