You need to invest $145,772 two times a year for 25 years to reach a savings goal of $500,000.
What is Accumulated amounts?
At the end of the loan period the borrower pays the lender the accumulated amount, which is equal to the sum of the principal plus interest.
Given
Interest rate = r = 5%
Compounding semi-annually = n = 2
Accumulated amount = A = $300,000
Number of years = t = 25
Accumulated and principle amounts in terms of compound interest is given by
[tex]P=\frac{A}{(1+i)^{N} }[/tex]
Where
i = [tex]\frac{r}{n}[/tex] = [tex]\frac{0.05}{2}[/tex] = 0.025
N = n × t = 2 × 25 = 50
[tex]P= \frac{500000}{(1+0.025)^{50} }[/tex]
P ≈ $145,772
Therefore, you need to invest $145,772 two times a year for 25 years to reach a savings goal of $500,000.
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