Amount

[Guest]

$50 / week is placed into a savings account, at 7% yield, for 40 years. Calculate amount.

7% = .07 (decimal form).

50 * 52 * 40 = 104000 (total investment).

Not sure how to solve.

[Guest]

This is called compound interest.
The formula is
P=initial principal balance = 52*50
r = interest rate = 0.07
y = years = 40
Final amount $= 52\times 50(1+0.07)^{40}$

[Guest]

52 * 50 (1+0.07)^40

52 * 50 (1.07)^40

52 * 50 * 14.9744

38933.44 = 38933

Answer indicated over half a million dollars. Where did I miscalculate ?

[Guest]

If times per year that interest will be compounded is 52(each week).
The formula is
[tex]52×50\times\left(1+\frac{0.07}{52}\right)^{40\times 52}[/tex]

[Guest]

52 * 50 ( 1 + 0.07 / 52) ^ 40 * 52

52 * 50 ( 1.07 / 52) ^ 40 * 52

2600 ( 1.07 / 52) ^ 2080

2600 * 0.0205769 ^ 2080

2600 * 6.7653417 = 17589.88 = 17590

Not sure about calculations.

[Baltuilhe]

Good afternoon and Merry Christmas!

First of all, interest rate:
[tex](1+i_w)^{52}=1+i_a[/tex]

[tex](1+i_w)^{52}=1+7\%[/tex]

[tex]1+i_w=(1+7\%)^{1/52}[/tex]

[tex]i_w=(1+7\%)^{1/52}-1[/tex]

[tex]i_w\approx 0,130197469\%p.w.[/tex]

Now, the Ammount:
[tex]FV=PMT\cdot\left[\dfrac{\left(1+i_w\right)^{n}-1}{i_w}\right][/tex]

[tex]FV=50\cdot\left[\dfrac{\left(1+i_w\right)^{52\cdot 40}-1}{i_w}\right]=50\cdot\left\{\dfrac{{\underbrace{\left[\left(1+i_w\right)^{52}\right]}_{1+i_a}}^{40}-1}{i_w}\right\}[/tex]

[tex]FV=50\cdot\left[\dfrac{\left(1+i_a\right)^{40}-1}{i_w}\right][/tex]

[tex]FV=50\cdot\left(\dfrac{1,07^{40}-1}{1,07^{1/52}-1}\right)[/tex]

[tex]FV\approx 536\,663,96[/tex]

[Guest]

Good evening and Merry Christmas!

A question:

What does the little "a" and "w" mean ?

[Baltuilhe]

w = week
a = annual

[Guest]

Thanks again.

[Guest]

Check my calculations:

Using $25 deposited weekly, using 7% interest.


25 * (1.07^40 - 1)
----------------
(1.07 ^ 1/52 - 1)

25 * 13.9744578
---------------
.0013019746


268331.99 = 268332

Answer given is more. Where did I miscalculate ?

[Guest]

Please reply, Thanks.