3 ms·
We have an infinite series such as: S = sum from (i=1) to infinity of [a^i] we can then multiply by a on each side: aS = sum from (i=1) to infinity of [a^(i+
by smabie 6y ago
We have an infinite series such as:
S = sum from (i=1) to infinity of [a^i]
we can then multiply by a on each side:
aS = sum from (i=1) to infinity of [a^(i+1)]
Simplify/cancel out to:
aS = S - a
a = S(1 - a)
S = a / (1 - a)
where a = 1 / (1 + R)
so $100 perpetuity with R = 5%:
a = 1 / (1 + 0.05) = 1 / (1.05)
$100 x (1/1.05) / (1 - (1/1.05)) = $100 x 1 / (1.05 - 1) = $100 / 0.05
= $100 / 5%
= $2000
- chadcmulligan 6y agoI've always thought this was the most useful equation I learnt at school - S = P (1+i)^n P - Principal S - Sum i - interest rate p.a. n - the number of years
- smabie 6y agoI always liked 58008