Question

HELP! Kate is saving for a vacation in the Bahamas. On January 1, she invested $750 at 8.2% per annum, compounded semi-annually. On July 1, she invested another $750 at the same rate. How much will she have from these investments on the next July 1st?

Answer 1

I tried P as the Principle invested: 750, i, as the interest rate per compounding period = 8.2/100 = 0.082 n, number of compounding periods = 2, and t, time is 6 (6 months before July 1 from January 1?) Because I got 1931.03 and it's wrong:

A = P(1 + i/n)^n(t)

The answer is suppose to be $1658. 84

Answer 2

Accumulated amount= 750(1+ 0.082/2)^3 + 750(1 + 0.082/2)^2

Answer 3

why did you do it like that?

Answer 4

why is the ^n(t) 3 and 2?

Answer 5

If it's compounded semi annually, the first 750 accumulates for 18 months, which is 3 half years. the second 750 accumulates for a year, which is 2 half years.

Answer 6

it accumulates for 18 months? and the second accumulates for a year? I understand the second accumulation but how is it 18 months for the first? And shouldn't it be 2.5 if it's half? sorry for asking so much question D;

Answer 7

Suppose she never made a second investment, how much would she have had on July 1 the second year? If she just had the starting investment

Answer 8

$846.08?

Answer 9

Yep. Now, if she only had one investment, on July 1 the first year, how much would she have the next year on July 1?

Answer 10

but why is it 3 and half years? What is the n and t?

And it's $812.77

Answer 11

add those too and you'll get the answer.

t = number of years
n = compounded per year

in the first one, 1.5 * 2 = 3 -- from jan1 to next year july1 is 1.5 years
the second one, 1 * 2 = 2 -- from july1 to next year july1 is 1 year

Answer 12

ohhhh, i get it! :P thank you!!

Answer 13

pleasure :)