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(b) If the Parent Decides Instead to Deposit a Lump Sum Now in Order to Attain the Goal of 100,000 in 10 Years, How Much Must Be

Question

(b) If the parent decides instead to deposit a lump sum now in order to attain the goal of 100,000 in 10 years, how much must be deposited now? Round your answer to two decimal places.

Solution

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Piper Veteran · Tutor for 12 years

Answer

Here's how to calculate the lump sum deposit needed:**Understanding Compound Interest**The formula for compound interest is:A = P(1 + r/n)^(nt)Where:* A = the future value of the investment/loan, including interest* P = the principal investment amount (the initial deposit or loan amount)* r = the annual interest rate (decimal)* n = the number of times that interest is compounded per year* t = the number of years the money is invested or borrowed for**Solving for P (Present Value)**We want to find P, so we rearrange the formula:P = A / (1 + r/n)^(nt)**Applying the Information**We're given:* A = 100,000 / (1 + 0.06/12)^(12*10)P = 100,000 / (1.005)^120P = 54,978.16**Answer**The parent must deposit approximately now.