Question

If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. Round up your answer to the next period.

Answer 1

It will take 3 years and 4 months to accumulate $ 28,500.

To determine, if an amount of $ 25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $ 28,500, the following calculation must be performed:

• 25,000 x (1 + 0.04 / 2) ^ (2X) = 28500
• 25000 x 1.02 ^ 2X = 28500
• 1.02 ^ 2X = 28500/25000
• 1.02 ^ 2X = 1.14
• 1.02 ^ 6.62 = 1.14
• 6.62 / 2 = X
• 3.33 = X

Therefore, it will take 3 years and 4 months to accumulate $ 28,500.

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