Answer:
These payments worth to me when I first start my college are$4,303.
Explanation:
Monthly Payments = P = $100
Interest rate = i = 5.5% = 0.055 = 0.055/12 = 0.00458
Number of years = 4 years
Period in a year = 12 months
Number of total periods = n = 4 x 12 = 48 periods
APV = P [ 1 - ((( 1 + i )^-n ) / i)]
APV = 100 [ (1 - (( 1 + 0.00458 )^-48 ) / 0.00458)]
Annuity present value = $4,303
The present value of $100 received each month for 4 years at the discounted rate of 8% will be
Present value refers to the current value of future sum. The present value tells the present worth of the amount to be received in future.
Annuity refers to a fixed sum that is paid for a fixed period constantly and at a fixed rate of interest.
The present value of annuity can be calculated as follows:
[tex]\rm P = PMT \times \dfrac{1- \dfrac{1} {(1+r)^n}} {r}[/tex] , where P is the present value, PMT is the periodic payment, r is the rate of interest and n is the number of times annuity is paid.
Given:
PMT is $100
r is 8%
n is 4 years which is 48 months
Therefore, the present value will be:
[tex]\rm P = 100 \times \dfrac{1- \dfrac{1} {(1+0.08)^{48}}} {0.08}\\\\\rm P = 100 \times \dfrac{1- \dfrac{1} {(1.08)^{48}}} {0.08}\\\\\rm P = \$ $4,303.[/tex]
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