Answer:
FIRST QUESTION
It will pay the bill after 7.45 = rounding 8 months, being the last payment less than 5,000
The total interest for the period will be 2,263.04
SECOND QUESTION The rate will be 6%
Step-by-step explanation:
for the first part, we should calculate the time it takes to an ordinary annuity of 5,000 to have a present value of 35,000 at discount rate of 18%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 5,000
time n
rate 0.015
PV $35,000.0000
[tex]5000 \times \frac{1-(1+0.015)^{-n} }{0.015} = 35000\\[/tex]
We work out the formula:
[tex](1+0.015)^{-n}= 1-\frac{35000\times0.015}{5000}[/tex]
We solve the right side of th formula
and then apply logarithmics properties:
[tex]-n= \frac{log0.895}{log(1+0.015)[/tex]
-n = -7.450765527
n = 7.45
It will pay the bill after 8 months.
Total Interest: we will build the loan schedule:
     Bill      Interest   Cuota&Amortization
1 Â Â Â 35000 Â Â Â Â 525& Â Â Â 5000 Â Â Â Â Â 4475
2 Â Â 30525 Â Â Â Â 457.88 Â Â 5000 Â Â Â Â 4542.12
3 Â Â 25982.88 Â 389.74 Â Â 5000 Â Â Â Â 4610.26
4 Â Â 21372.62 Â 320.59 Â Â 5000 Â Â Â Â 4679.41
5 Â Â 16693.21 Â 250.4 Â Â Â 5000 Â Â Â Â Â 4749.6
6 Â Â 11943.61 Â Â 179.15 Â Â Â 5000 Â Â Â Â Â 4820.85
7 Â Â Â 7122.76 Â Â 106.84 Â Â 5000 Â Â Â Â Â 4893.16
8 Â Â Â 2229.6 Â Â 33.44 Â Â Â 2263.04 Â Â Â 2229.6
Total        2263.04  37263.04    35000
The total interest for the period will be 2,263.04
Second question we will solve for the rate at which a capital of 3,000 returns 5,372.54 after 10 years
[tex]Principal \: (1+ r)^{time} = Amount[/tex]
Principal 30,00.00
Amount = 5,372.54
time 10.00
rate ?
[tex]3,000 \: (1+ r)^{10} = 5,372.54[/tex]
[tex]r = \sqrt[10]{5,372.54/3,000} - 1 [/tex]
r = 0.059999939 = 0.06 = 6%
