Question

MY NOTES PRACTICE ANOTHER Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) $1300/semiannual period for 5 yr at 12%/year compounded semiannually $ Need Help? Read it Tuto a Tutor 5. [0/0.1 Points] DETAILS PREVIOUS ANSWERS TANAPMATHS 4.2.014 MY NOTES PRACTICE ANOTHER Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) $130/month for 14 yr at 7%/year compounded monthly $ 222.86 X Need Help? Read Tu te Tutor 6. [-/0.1 Points] DETAILS TANAPMATHS 4.2.016.MI. MY NOTES PRACTICE ANOTHER If Jackson deposits $200 at the end of each month in a savings account earning interest at a rate of 9/year compounded monthly, how much will he have on deposit in his savings account at the end of 4 yr, assuming he makes no withdrawals during that period? (Round your answer to the nearest cent.)

Answer 1

4.

Given,

Semi annual payment = $1300

Interest rate = 12% or 0.12

Number of years = 5 years

Solution :-

Semi annual interest rate (r) = 0.12/2 = 0.06

Semi annual periods (n) = 5 years x 2 = 10

Now,

Present value of the ordinary annuity

= Semi annual payment/r x [1 - (1 + r)^-n]

= $1300/0.06 x [1 - (1 + 0.06)^-10]

= $1300/0.06 x [1 - (1.06)^-10]

= $1300/0.06 x [1 - 0.5583947769]

= $1300/0.06 x 0.4416052231

= $9568.11

Answer 2

SOLUTION :

First problem :

Period of compounding : semiannually.

Interest rate per period, r = 12/2 = 6% = 0.06

=> 1 + r = 1.06

No. of periods, n = 5 * 2 = 10 semi-annual periods.

Annuity , A = $1300 per period.

So,

PV 

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

= 1300(1.06^10 - 1)/(0.06*1.06^10)

= 9568.11 ($) 

PV of the given annuity = $9.568.11 (ANSWER).

Second problem :

Period of compounding : monthly.

Interest rate per period, r = 7/12 % = 7/1200

=> 1 + r = 1207/1200

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

Annuity , A = $130 per period.

So,

FV 

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

= 130((1207/1200)^168 - 1)/((7/1200)*(1207/1200)^168)

= 13897.79 ($) 

FV of the given annuity = $13,897.79  (ANSWER).