4 ms·
> simply taking the payment divided by the interest rate to discount it with Looks right, but do you have a proof?
by tantalor 6y ago
> simply taking the payment divided by the interest rate to discount it with
Looks right, but do you have a proof?
- smabie 6y agoWe 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