The interest is compounded in the investment and the fees, the 4 years
school fees is however larger than the future value of the investment.
Response:
First part:
The future value, FV, of the investment after 18 years is given as follows;
Where;
PV = The present value = $10,000
i = The interest rate = 8% = 0.08
n = The number of years = 18
Which gives;
[tex]FV = 10,000 \times (1 + 0.08)^{18} \approx \mathbf{39,960.195}[/tex]
The future value of the investment, FV = $39,960.195
The school fees each year is given as follows;
Fees = First year fees·(1 + r)ⁿ
Where;
First year fees = $12,000
r = Increase rate of the school fees = 11% = 0.11
n = The number of years
The school fees for four years is given as follows;
∑Fees = $12,000 + $12,000·(1 + 0.11) + $12,000·(1.011)² + $12,000·(1.011)³
Which gives;
∑Fees = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² +12,000·(1 + 0.11)³ = 56,516.772
The total tuition fees for four years = $56,516.772
The future value of the investment after 18 years, $39,960.195 is less
than the amount required as school fees for four years, therefore;
Second part:
The fees for 3 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^3[/tex] = 12,000 + 12,000·(1 + 0.11) + 12,000·(1 + 0.11)² = 40,105.2 > 39,960.195
The fees for 2 years of school is given as follows;
[tex]\displaystyle \sum \limits_{n = 1 }^2[/tex] = 12,000 + 12,000·(1 + 0.11) = 25,320 < 39,960.195
The number of years of college the value of the investment will take care of is therefore;
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