Question

Annuity question.
Steve deposits $50.00 each week into a bank account that earns 5.75% interest, compounded weekly. How much money will he have saved after 90 weeks?
@AravindG

Answer 1

well the future value of an annuity is

\[A = \frac{M[(1 + r)^n -1]}{r}\]

M is the contribution paid at the end of the period.

r is the interest rate as a decimal

n = number of time periods.

Answer 2

so the interest is per annum... you need to convert it to weekly then change it to a decimal.

The formula above is for a annuity paid at the end of the period.

Answer 3

convert the equation ?

Answer 4

well you need to find the interest and find out when the regular payment is made... start or end of the week as it affects the future value.

Answer 5

50[(1+0.0575)90 -1] / r
50[(1.0575)^90-1]/r

? ... can't you tell I'm awful with math

Answer 6

you forgot 0.575 in the denominator...

and you'll get an answer... but the question is extremely poor with information.

Answer 7

is it 0.575 or 0.0575

Answer 8

5.75% = 0.0575

Answer 9

okay

Answer 10

N = total number of payments
I = annual interest rate (as percent, NOT decimal)
PV = present value
PMT = regular payment amount
FV = future value
P/Y = payment periods per year (annual =1, monthly = 12, quarterly = 4, etc.)
C/Y = compounding periods per year
PMT: this is always END for ordinary annuities


A=P[(1+r)n−1]/r
A= 50[(1.0575)^90-1]/0.0575
A=50(152.19)/0.0575
A=7609.56/0.0575
????? is this right so far or am I completely wrong

Answer 11

@mathslover

Answer 12

someone help...
please

Answer 13

how much does he have in his account at the end of the first week if he deposits $50 into his account at the end of the week??

Answer 14

.... this is a method to determine a recurrsion that develops the formula.

Answer 15

0 week1 0k 50
|---------------|----| = 50


50 week2 50k 50
|---------------|----| = 50k + 50


50k + 50 week3 (50k+50)k 50
|--------------------|--------| = 50k^2 + 50k + 50


i see a pattern forming such that: for the nth week, he will have:

50k^(n-1) + 50k^(n-2) + ... + 50 in the account

we can factor out the 50 and the rest becomes a geometric sum

50(1 + k^2 + k^3 + ... + k^(n-1))

Answer 16

a geometric sum can be proofed out into the formula: (1-k^n)/(1-k)

Answer 17

the value for k is the compounding factor (1+r/52) in this case