Question 1193351
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We break things up into two pieces.
Part (i): Depositing $2400 per month for 48 months (aka 4 years)
Part (ii): Letting the money sit another 9 years, without any further deposits


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Part (i)
Apply the future value of annuity formula.
FV = P*( (1+i)^n - 1 )/i


P = 2400 = deposit per month
i = r/12 = 0.03/12 = 0.0025 = interest rate per month in decimal form
n = 4*12 = 48 = number of months


FV = P*( (1+i)^n - 1 )/i
FV = 2400*( (1+0.0025)^48 - 1 )/0.0025
FV = 122,234.900198333
FV = 122,234.90
After the four years are up, the account will have a balance of $122,234.90


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Part (ii)
This amount is the starting deposit P in the compound interest formula below.
We use n = 12 to refer to compounding monthly
A = P*(1+r/n)^(n*t)
A = 122,234.90*(1+0.03/12)^(12*9)
A = 160,069.430989373
A = 160,069.43
This is the final balance after another 9 years go by (4+9 = 13 years total).
This includes the principal deposits plus interest earned.


Let's say the account didn't earn any interest.
Depositing $2400 for 48 months means the account would have a balance of 48*2400 = 115,200 dollars


Therefore, the total interest earned is 160,069.43 - 115,200 = 44,869.43 dollars.


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Answers:


a) $160,069.43


b) $44,869.43
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