Question 1193351: $2,400 was deposited at the end of every month for 4 years into a fund earning 3% compounded monthly. After this period, the accumulated money was left in the account for another 9 years at the same interest rate.
a) Calculate the accumulated amount at the end of the 13-year term. $
b) Calculate the total amount of interest earned during the 13-year period. $
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
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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