PLs HELP me OUT MATHEMATICIANS and EXperts!!?

Question

i know the trick behind this simple interest problems but i can't arrive at the final answer. i'm doing someti

1, We borrowed $5000 for two years, with a simple annual interest rate of 8%. After 8 months, we
make a partial payment of $1000. After an additional 8 months, we make another partial payment
of $1000. How much do we have to pay at the end of the two years?

$5000(1+0.08 *8/12)= 526.67
526.67-1000=473.33
473.33( 1+0.08 *8/12)= 498.57
498.57-1000
501.43(1+0.08 *8/12)
=$528.17 Which is my final answer but it's wrong i don't know why

2, We borrowed $1000 for a year, with a simple annual interest rate of 8%. After 5 months, we make a
partial payment of $300. After an additional 3 months, we make another partial payment of $350.How much do we have to pay at the end of the year?

1000(1+0.08 * 5/12)=1033.33
1033.33-300
733.33(1+0.08 * 3/12)= 747.10
747.10-350
397.1(1+0.08 *4/12)= 407.69
$407.69 was my final answer which is WRong. The correct answer is $ 408.6

Answer 1

Your arthimetic is wrong.

#1)
$5000(1+0.08 *8/12)= 526.67 IS WRONG.

Should be = 5266.67

Work back through it from there and you should have it right.

#2)
733.33(1+0.08 * 3/12)= 747.10 is wrong

should be = 747.99

Answer 2

5000(1 + .08•2/3) = 5000(1.0533333) = 5266.67
5266.67-1000 = 4266.67
4266.67(1.0533333333) = 4494.22
4494.22-1000 = 3494.22

In your #1, you got the decimal in the wrong place.

Another possibility for error: all this assumes the annual interest is prorated and computed at the time the payment is made. But is it? Could the interest only be computed at the end of the year on the balance at that time? Also, the process we used ADDS the interest to the balance, which produces a compounding effect. Credit cards define an "average daily balance" on which to compute interest charges. Should something like that be done here? There's a reason for all that fine print on the back of the credit card bill. All this stuff has to be spelled out (which it isn't in your problem) or people misunderstand and sue.