Thread: Geometric series problems - finding future values of annuities

Hello. I'm having some difficulties with these questions and I'd like to know what I'm doing wrong:

1. $4300 is deposited at the end of every 6 months for 7 years at 9.5%/a, compounded semiannually. Find the amount of this annuity on the date of the last payment.

What I'm doing:

FV = 4300((1.0475)^14) - 1) / .0475
FV = 4300(0.91494) / .0475
FV = 3934.266/.0475
FV = 82,826.66

But the answer in the back of the book is 81,408.07.

Also having problems with this question:

2. At the end of each month, $50 is deposited in an account for 25 years. Then the accumulated money remains in the account for an additional 5 years. Find the amount in the account at the end of this time. The interest rate is 4.8%/a, compounded monthly.

FV = 50((1.0033^300) - 1)/0.0033
FV = 50(1.68652)/0.0033
FV = 84.34258/0.0033
FV = 25,558.36

A = 25558.36(1.0033^60)
A = 25558.36(1.2186)
A = 31,144.53

but the answer is $36,724.36. I would really appreciate some help with these questions.

Hi fiftybirds,
Problem 2
The sinking fund factor applies to the first 25 years
Compound amount factor applies to that earned in the next 5 years
SF S = R (( 1+ i)^n -1 )/i
CA =(1+i) ^n * S
n = 300 and i = 0.004 for S
n = 5 and i =0.048 for CA. I get an answer close to your post

Hello, fiftybirds!

1. $4300 is deposited at the end of every 6 months
for 7 years at 9.5%/annum, compounded semiannually.
Find the amount of this annuity on the date of the last payment.

What I'm doing:



. . .

But the answer in the back of the book is 81,408.07.

I agree with your answer.

2. At the end of each month, $50 is deposited in an account for 25 years.
The interest rate is 4.8%/annum, compounded monthly.
Then the accumulated money remains in the account for an additional 5 years.
Find the amount in the account at the end of this time.

. . . . . wrong interest rate
. . . . . . . . . .


. .

But the answer is $36,724.36.

Hello again fiftybirds.
I rechecked and found mistakes so my new answer is considerably higher.I think my equations are correct

Originally Posted by fiftybirds

FV = 82,826.66
But the answer in the back of the book is 81,408.07.

You're correct. Book's answer uses 9%.

Originally Posted by fiftybirds

A = 31,144.53
but the answer is $36,724.36.

Book is correct. You should use 1 + .048/12 = 1.004;
looks like you did this: 1 + .04/12 = 1.00333....

My use of a calculater this evening is a bit faulty.
I calculate the sinking fund factor is 578.045, the compound amount factor is 1.26417
the final amount is 50 x 578.045x 1.26417= $36537.36.If this is wrong I would like to know what I am doing wrong

Originally Posted by bjhopper

... the compound amount factor is 1.26417

1.004^60 = 1.27064...

Hello again. Thanks for your replies, they really helped me. However I'm now doing present value and I'm having difficulties again... I'm not sure how to approach these problems:

1. Steven wants to purchase a speedboat that sells for $22,000. The dealer offers a $2000 discount if Steven pays the total amount in cash, or a finance rate of 2.4%/a, compounded monthly, if Steven makes equal monthly payments for 5 years. To pay for the boat with cash now, Steven knows he can borrow the money from the bank at 6%/a, compounded monthly, over the same 5 year period. Which offer should he choose?

2. Rene buys a computer for $80 down and 18 monthly payments of $55. The first payment is due next month. What is the selling price of the computer system?

thank you

Originally Posted by fiftybirds

2. Rene buys a computer for $80 down and 18 monthly payments of $55. The first payment is due next month. What is the selling price of the computer system?

0% rate?

Note: It is better to start a new thread when posting a new problem.

Originally Posted by fiftybirds

1. Steven wants to purchase a speedboat that sells for $22,000. The dealer offers a $2000 discount if Steven pays the total amount in cash, or a finance rate of 2.4%/a, compounded monthly, if Steven makes equal monthly payments for 5 years. To pay for the boat with cash now, Steven knows he can borrow the money from the bank at 6%/a, compounded monthly, over the same 5 year period. Which offer should he choose?

Loan Payment formula: P = Ai / (1 - x) where x = 1 / (1 + i)^n

P = Payment (?)
A = Amount borrowed (22000)
n = number of periods (60)
i = interest rate per period (.024 / 12)