Question

Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) 

$1500/semiannual period for 9 yr at 6%/year compounded semiannually 

Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) 

$130/month for 15 yr at 11%/year compounded monthly 

Answer 1

SOLUTION :

First problem :

Period of compounding : semiannually.

Interest rate per period, r = 6/2 = 3% = 0.03

=> 1 + r = 1.03

No. of periods, n = 9 * 2 = 18 semi-annual periods.

Annuity , A = $1500 per period.

So,

FV 

= A((1+r)^n - 1)/r

= 1500(1.03^18 - 1)/(0.03)

= 35121.65 ($) 

FV of the given annuity = $35,121.65 (ANSWER).

Second problem :

Period of compounding : monthly.

Interest rate per period, r = 11/12 % = 11/1200

=> 1 + r = 1211/1200

No. of periods, n = 15 * 1 2 = 180 months

Annuity , A = $130 per period.

So,

FV 

= A((1+r)^n - 1)/r

= 130((1211/1200)^180 - 1)/(11/1200)

= 59109.64 ($) 

FV of the given annuity = $59,109.64 (ANSWER).