1. The formula of accumulated value is
Here AV is the accumulated value, P is the amount to be invested today, r is the rate of return, m is the number of times money is compounded in per unit of n, n is the number of years
So, we have the following details:
r = 5%
AV = $8000
n = 3 years
Since the money is compounded semi-annually, m = 2
So, we need to find P. If we plug in the numbers in the formula, we'll get
$8000 = P( 1 + (0.05/2))(3*2)
$8000 = P(1.025)6
Using calculator we find the value of 1.0256 is 1.160 approx
So, $8000 = P * 1.160
Dividing both sides by 1.160, we get
8000/1.160 = (P * 1.160)/1.160
So, 8000/1.160 = P i.e. P = $6896.55
So, the amount to be deposited is $6896.55
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