I need help solving these problems or providing a formula for each would help.?

Question

1. The Flores Family loves to go sailing on the weekends.  Mr. Flores has decided to purchase a more spacious sailboat.  The sailboat he is interested in buying in 2 years will cost him $20,000.  An account at Invest Well Bank earns 6% per year compounded monthly.  How much should Mr. Flores deposit in this account at the beginning of each month to be able to pay cash for the sailboat in 2 years?
a) $935.16
b) $747.06
c) $845.78
d) $816.41
e) $786.41
f) None of the above.

2. A school realizes that they need a new copy machine for their main office.  The copy machine costs $4,500.  After speaking with the financial advisor, they decide to pay 20% of the cost of the machine in cash and finance the rest through their credit union.  How much is their monthly payment if the credit union will charge 2% per year compounded monthly for 3 years?
a) $23.09
b) $99.87
c) $103.11
d) $113.11
e) $33.09
f) None of the above.

3. Your brother would like to have $27,000 in 2 years for the purchase of a new car.  What monthly payment should he make into an account paying 6% per year compounded monthly to attain his goal?
a) $1,091.66
b) $1,061.66
c) $1,081.66
d) $1,071.66
e) $1,031.66
f) None of the above.

4. You borrowed $11,000 from your bank to build a small cabin on your property.  The bank will charge 6% per year compounded quarterly.  You decide to payoff this loan in 2 years by making quarterly payments.  How much are your quarterly payments?
a) $1,449.42
b) $1,469.42
c) $1,499.42
d) $1,479.42
e) $1,439.42
f) None of the above.

Thanks!

M3 · Accepted Answer

you should manage with 2 sets of formulas

FV = PMT((1+r)^n - 1)/r
this will apply to q1 & 3
PMT = PVr(1-(1+r)^-n) 
this will apply to q2 & q4

FV = future value, PV = present value (loan to be financed)
if r = 6% p.a. for 5 years , and payments/compounding  are, say, monthly, r = 0.06/12, n = 12*5

applying these formulas, the answers are
1) 20,000*.005/((1.005^24-1) => e
2)  (4500*.8)*(.02/12)/(1-(1+.02/12)^-36) => c
3) 27000*.005/(1.005^24-1) => b
4) do at least one by yourself !

Jonathan · Answer

The basic formula =
Tv=Iv(1+(R/100C))^CT
Tv=total value
Iv=initial value
R=rate (percent)
C=compounds per year (monthly=12, semi=2, etc)
T=number of years

Now I'll only do the odds, to give you an idea of what to do...
1. Need to find a. the initial value, and b. (more importantly) the deposit each month.
Plug in all known information.
20,000=Iv(1+(6/(12(100))))^12(2)
20,000=Iv(1.005)^24
17743.71=Iv

Divide by 24 months to get the required monthly amount.
=$739.32
None of the Answers above.

3. Same Idea as the first question
27,000=Iv(1+(6/(12(100))))^12(2)
27,000=Iv(1.005)^24
23954.01=Iv

Divide by 24 months to get the monthly amount. (again)
=998.08
Again, None of the Above

I'm not sure if this is the right way, but hope it helps!

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I need help solving these problems or providing a formula for each would help.?

2 Answers