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You need to invest $145,772 two times a year for 25 years to reach a savings goal of $500,000.
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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