Respuesta :
Answer:
Explanation:
The formula for calculating the Monthly payments P for the sinking fund is as follows:
[tex]P\;=\;\frac{A*i}{(1+i)^n-1}[/tex]
where,
P = Monthly payments to be made
A = Total amount to be accumulated
i = Interest rate for given time period
n = Number of time period
Assuming interest is applied at the beginning of each period.
We are given two scenarios.
Scenario (i) - Deposit is made during the year:
In this scenario, as some of the year is already passed (assume 6 months), to complete the time period of 3.5 years the interest will compound 3 times (as the 0.5 year payments can be adjusted in the remaining part of the first year and no interest is applied on it). Hence, the interest will be applied 3 times.
[tex]\therefore P_{(i)}\;=\;\frac{5000*0.08}{(1+0.08)^3-1}\\\\P_{(i)}\;=\;\frac{400}{0.2597}\\\\P_{(i)}\;=\;1540.1676[/tex]
Scenario (ii) - Deposit is made at the beginning of the year:
For this case, the interest will be applied 4 times to complete the time period of 3.5 years for payment.
[tex]\therefore P_{(ii)}\;=\;\frac{5000*0.08}{(1+0.08)^4-1}\\\\P_{(ii)}\;=\;\frac{400}{0.3605}\\\\P_{(ii)}\;=\;1109.6040[/tex]
