{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ACTSC 231 tutorial

# ACTSC 231 tutorial - Problem Set 6 ACTSC 231 Mathematics of...

This preview shows pages 1–2. Sign up to view the full content.

Problem Set 6: ACTSC 231 Mathematics of Finance, Winter 2011 Q1. Payments are made into an account continuously at a rate of 8 Y + tY per year, for 0 t 10. At time T = 10, the account is worth \$20, 000. Find Y if the account earns interest according to a force of interest δ t = 1 / (8 + t ) at time t , for 0 t 10. Q1. The accumulated value at T = 10 of the annuity is 10 0 (8 Y + tY ) m ( t ) dt, where m ( t ) is the accumulated factor over period [ t, 10] so that m ( t ) = exp 10 t δ r dr = exp 10 t ( r + 8) - 1 dr = exp ln( r + 8) 10 r = t = 18 t + 8 . Thus, its accumulated value is equal to 10 0 (8 Y + tY ) 18 t + 8 dt = Y 10 0 18 dt = 180 Y. Equating 180 Y to 20,000, we obtain Y = 20 , 000 180 = 111 . 11 . Note: Students may first develop an expression for the present value and then compute the accumulated value by the formula AV = PV · a (10). Q2. A 2-year deferred annuity paying continuously at a rate of 300 + 200 t per year, for 2 t 10. Find the present value of this annuity, if the force of interest function δ t = 5 / (3 + 2 t ) for 0 t 10.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}