Question

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

$1400/semiannual period for 8 yr at 9%/year compounded semiannually 

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

$100/month for 14 yr at 15%/year compounded monthly

Answer 1

SOLUTION :

First problem :

Period of compounding : semiannually.

Interest rate per period, r = 9/2 = 4.5% = 0.045

=> 1 + r = 1.045

No. of periods, n = 8 * 2 = 16 sem-iannual.

Annuity , A = $1400 per period.

So,

FV 

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

= 1400(1.045^16 - 1)/(0.045)

= 31807.07 ($) 

FV of the given annuity = $31,807.07  (ANSWER).

Second problem :

Period of compounding : monthly.

Interest rate per period, r = 15/12 = 1.25% = 0.0125

=> 1 + r = 1.0125

No. of periods, n = 14 * 1 2 = 168 months

Annuity , A = $100 per period.

So,

FV 

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

= 100(1.0125^168 - 1)/(0.0125)

= 56484.50 ($) 

FV of the given annuity = $56,484.50 (ANSWER).

Answer 2

.I hope you have got your answer , if you need any further clarification in any step, please let me know through comment.

A = 1400 t = 8 years rate , x = 99% =0-09 - 2 (compounded semi-an Future value is given by FV = 1400 ((1+0.89) 28_17 = 1400 0.09/2 - 1400 [22.7193367] - 31807-07 @ A= 100 t = 14 yrs =15070 = 0.15 n=12 12x14 + 12 FV = 100 ((1+ 0.15) 12x14 17 I 0.15/12 - 1 S Joox (564.845011) = 56484.50