Question

Find the lump sum deposited today that will yield the same total amount as this yearly payment (made at the end of each year for 20 years at the given interest rate, compounded annually).

Answer 1

$129,108.10

Step-by-step explanation:

Missing word "$9500 at 4%"

Present Value of the amount to be deposited P = ?

Annual Year end payment A = $9,500

Rate of interest r = 4% compounded annually

Period of payment n = 20 years

P = A * [1- (1/(1+r)^n)] / r

P = $9500 * [1 - (1/(1+0.04)^20)] / 0.04

P = $9500 * [1-(1/(1.04)^20)] / 0.04

P = $9500 * [1 - (1/2.191123143)] / 0.04

P = $9500 [1 - 0.45638695] / 0.04

P = $9500 * 0.5436131 / 0.04

P = $9500 * 13.590326

P = $129,108.1003

P = $129,108.10

So, the lump sum deposited today is $129,108.10.