A bank offers 5% compounded weekly. How much should be deposited now in order to have $3,000 in four years?State your answer to the nearest $1
.05 / 365 = r
4*52 = 208 = n
x (1+r)^n = 3000
x = 3,000/(1+r)^n
r = 0.05/52.
yes r = 0.05/52
weekly not daily !
To find out how much should be deposited now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the future amount (in this case, $3,000)
P is the principal amount (the current amount to be deposited)
r is the annual interest rate (5%, or 0.05)
n is the number of times the interest is compounded per year (52, since it is compounded weekly)
t is the number of years (4)
Let's substitute these values into the formula and solve for P:
3000 = P(1 + 0.05/52)^(52*4)
First, let's simplify the exponent:
3000 = P(1.000962524)^208
Next, let's calculate the exponential part:
(1.000962524)^208 = 1.236095
Now, let's solve for P:
3000 = P * 1.236095
Divide both sides by 1.236095:
P ≈ 2427.82
Therefore, approximately $2,427 should be deposited now in order to have $3,000 in four years.