Question

A University is oflexing a chartable git program A former student who is now 50 years old is cosider the following offer The student can invest 59),200 00 today and hen will be pad a Using the students desired retum, what is the value of this delerred annuity today on his 50th brthday? Answer Fomat: Currency: Round to: 2 decimal places Enter Answer Here 0峊自田

Answer 1

A = Annuity = APR x Investment = 8.00% x 9,200 = $ 736

He is currently on his 50th birthday. First payment comes on 65th birthday which is 15 years away from today and the last payment comes 20 years after his 65th birthday that is 20+15 = 35 years from today

Desired return, r = 6%

Hence, value of these annuity today = PV of all the future annuities = A /(1+r)¹⁵ + A / (1+r)¹⁶ + ....A / (1+r)³⁵

$=\frac{A}{(1+r)^{15}}\times (\frac{1-(1+r)^{-20}}{1- (1+r)^{-1}})=\frac{736}{(1+0.06)^{15}}\times (\frac{1-(1+0.06)^{-20}}{1- (1+0.06)^{-1}})$

= $ 3,733.84