Question

Solve the problem. 20) You have a $4286 credit card debt, and you plan to pay it off through monthly payments of S80. If you are being charged 13% interest per 20 year, how long (to the nearest tenth of a year) will i take you to repay your debt? Find the present value of the ordinary annuity. 21)Payments of $3300 made annually for 2) 25 years at 7% compounded annually Find the future value of the annuity due. 22)_ 22) 5200 deposited at the beginning of each quarter for B years at 4 compounded quarterly 23)- Find the APY corresponding to the given nominal rates. 23) 4% compounded quarterly 24) Solve the problem. 24) How long must $4500 be in a bank at 7% compounded annually to amount initially placed in savings, t is the time in years, and Pt) is the balance after time t. Round to the nearest year.) become $8852.18? (Use the function P(t)-Poekt, where Po is the 25) Find the future value of the loan. 25) $7600 loan at 5.5% for 9 months

Answer 1

Answer:

20)

Given

Loan amount L=$4286

Monthly payment P=$80

annual interest rate =13%

Monthly interest rate r= 13%/12=1.083

Let N be the number of months

So L=P*(1-(1+r)^-N)/r

4286=80*(1-(1+1.083%)^-N)/1.083%

(1+1.083%)^-N=0.4197

N=80.58 months

Years = N/12=6.7 years

21)

Given

Annual Payment P=$3300

N=25 years

r=7%

So Present value PV=P*(1-(1+r)^-N)/r

PV=3300*(1-(1+7%)^-25)/7%

PV=$38456.82

22)

Given

Annual Payment P=$200 each quarter

N=8*4=32 quarters

Annual rate =4%

Quarterly rate r=4%/4=1%

So Future value of annuity due FV=P*(1+r)*((1+r)^N-1)/r

FV=200*(1+1%)*((1+1%)^32-1)/1%

FV=$7573.80

23)

Given

Annual Nominal Rate =4%

Per quarter rate R=4%/4=1%

APY=(1+R)^4-1=(1+1%)^4-1=4.06%