joanne made semi-annuall deposits of $820 into a savings account.For the first 4years interest was 5%?

Question

compounded semi-annually.Since then the rate of interest has been 3.9% compounded semi-annually,How much is the account balanceafter eleven years?

Answer 1

The *right* way to figure this out is to use an algebraic
formula, but I think it's easier to visualize if you use a
spreadsheet.

It's slightly difficult to present a table in Yahoo Answers
because everything is jammed hard against the left
margin. [I'm not sure why that's a feature.] To help
reduce the column misalignment, I displayed all of the
numbers with a constant width (ie. with leading zeros
when necessary). Bottom line is that you'd have
$30344.87 at the end of eleven years.

Year == years since start of account (in half year increments)
Rate == interest rate
Balance == running balance of account
Interest == interest payment for previous 6 months


Year Deposit Rate Balance Interest

00.00 820.00 0.000 00820.00 0000.00
00.50 820.00 1.050 01681.00 0041.00
01.00 820.00 1.050 02585.05 0084.05
01.50 820.00 1.050 03534.30 0129.25
02.00 820.00 1.050 04531.02 0176.72
02.50 820.00 1.050 05577.57 0226.55
03.00 820.00 1.050 06676.45 0278.88
03.50 820.00 1.050 07830.27 0333.82
04.00 820.00 1.050 09041.78 0391.51
04.50 820.00 1.039 10214.41 0352.63
05.00 820.00 1.039 11432.77 0398.36
05.50 820.00 1.039 12698.65 0445.88
06.00 820.00 1.039 14013.90 0495.25
06.50 820.00 1.039 15380.44 0546.54
07.00 820.00 1.039 16800.28 0599.84
07.50 820.00 1.039 18275.49 0655.21
08.00 820.00 1.039 19808.23 0712.74
08.50 820.00 1.039 21400.76 0772.52
09.00 820.00 1.039 23055.38 0834.63
09.50 820.00 1.039 24774.54 0899.16
10.00 820.00 1.039 26560.75 0966.21
10.50 820.00 1.039 28416.62 1035.87
11.00 820.00 1.039 30344.87 1108.25

Additional comment:

Oh man, I messed this up. Thanks to "Mark Taranto"
for catching and correcting my mistake.

I took yet another look at this and want to
work through it carefully. We appear to have
as many different answers as there are people
submitting solutions.

On day 1, Joanne put in $820, so that's her's balance.

After 1/2 year, the bank would add half of 5% interest,
which is 820*.025 = 20.50 and Joanne would add another
$820. So after six months, she would have:

$820 + $20.50 + $820 = $1660.50


After one year, the bank will again add half of 5% as
interest, which would be $1660.50 * 0.025 = $41.51.
Then Joanne would add $820, so the new total would be:

$1660.50 + $41.51 + $820 = 2522.01

Continuing this process in the spreadsheet, the
final result after 11 years is:

$23809.46

The corrected spreadsheet follows:

Year Deposit Rate Balance Interest

00.0 820.00 0.0000 00820.00 000.00
00.5 820.00 0.0250 01660.50 020.50
01.0 820.00 0.0250 02522.01 041.51
01.5 820.00 0.0250 03405.06 063.05
02.0 820.00 0.0250 04310.19 085.13
02.5 820.00 0.0250 05237.94 107.75
03.0 820.00 0.0250 06188.89 130.95
03.5 820.00 0.0250 07163.62 154.72
04.0 820.00 0.0250 08162.71 179.09
04.5 820.00 0.0250 09186.77 204.07
05.0 820.00 0.0195 10185.92 179.14
05.5 820.00 0.0195 11204.54 198.63
06.0 820.00 0.0195 12243.03 218.49
06.5 820.00 0.0195 13301.77 238.74
07.0 820.00 0.0195 14381.15 259.38
07.5 820.00 0.0195 15481.59 280.43
08.0 820.00 0.0195 16603.48 301.89
08.5 820.00 0.0195 17747.24 323.77
09.0 820.00 0.0195 18913.31 346.07
09.5 820.00 0.0195 20102.12 368.81
10.0 820.00 0.0195 21314.12 391.99
10.5 820.00 0.0195 22549.74 415.63
11.0 820.00 0.0195 23809.46 439.72

Answer 2

$820 every half a year? first four years interest is 5% semi-annually?

so first four year, joanne will deposit total $820 x 4 yrs x 2 times per years = $6560. But will 5% semi-annual interest, the total saving including interest will be $9,433.30 in end of fours years

from fifth to eleventh years, continue $820 every half a year with 3.9%: totaly saving will be $31,594.76

Total deposit $18,040.00. Interest earn $13,554.76

Answer 3

Morgan's solution is correct -- except for one problem. Morgan is giving you a full year's interest every six months.

Since you get 5% on your investment in the first years, that means you are credited with 5%/2 or 2.5% every six months. Similarly, when the rate changes to 3.9% per year, that means you get 1.95% every six months.

The result is that the amount in the bank at the end of the 11th year is $1,655.99. This assumes that yout first payment of $820 is now.

Answer 4

4.10 + 223.86 =227.96 rounded 228.00
I think but I'm not sure

Answer 5

$2.
SUCKY SUCKY