Answer:
The semi annual payment is $4144.95
Step-by-step explanation:
Given as :
The price of computer software = $5,200
The down payment amount = $1000
So, The rest amount after down payment = $5,200 - $1,000 = $4,200
Now, The principal amount of finance = p = $4,200
The rate of interest = r = 12%
The time period of loan = t = 6 years
Let The Amount after 6 years = $A
<u>Now, From compounded method</u>
Amount = Principal × ![(1+\dfrac{\textrm rate}{ 100})^{ \textrm time }](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20rate%7D%7B%20100%7D%29%5E%7B%20%5Ctextrm%20time%20%7D)
Or, A = p × ![(1+\dfrac{\textrm r}{ 100})^{ \textrm t }](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%20r%7D%7B%20100%7D%29%5E%7B%20%5Ctextrm%20t%20%7D)
Or, A = $4,200 × ![(1+\dfrac{\textrm 12}{100})^{ \textrm 6 }](https://tex.z-dn.net/?f=%281%2B%5Cdfrac%7B%5Ctextrm%2012%7D%7B100%7D%29%5E%7B%20%5Ctextrm%206%20%7D)
Or, A = $4,200 × ![(1.12)^{6}](https://tex.z-dn.net/?f=%281.12%29%5E%7B6%7D)
Or, A = $4,200 × 1.9738
∴ A = $8289.9
So, The semi annual payment = ![\dfrac{\textrm Amount}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%20Amount%7D%7B2%7D)
Or, The semi annual payment = ![\dfrac{\textrm 8289.9}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctextrm%208289.9%7D%7B2%7D)
∴ The semi annual payment = $4144.95
Hence, The semi annual payment is $4144.95 Answer