**Question:**At a 6% annual effective interest rate, how much money will be accumulated in 10 years for an initial investment of $1,000?The answer is most nearly:- $1,200- $1,400- $1,600- $1,800**Analysis:**To solve this, we apply the formula for compound interest:\[ A = P (1 + r)^n \]Where:- $ A $ is the amount of money accumulated after n years, including interest.- $ P $ is the principal amount (initial investment).- $ r $ is the annual interest rate (decimal).- $ n $ is the number of years the money is invested.**Calculation:**For this problem, the values are:- $ P = 1,000 $- $ r = 0.06 $- $ n = 10 $Plug the values into the formula:\[ A = 1,000 (1 + 0.06)^{10} \]\[ A = 1,000 (1.06)^{10} \]\[ A = 1,000 \times 1.790847 \]\[ A \approx 1,790.85 \]Thus, the answer is most nearly $1,800. ### Present Value Calculation ExampleYou are expected to receive $2,000 six years from today. Assuming a 3% effective annual interest rate over the six-year period, the equivalent present value of that money today is most nearly:- $1,620- $1,640- $1,660- $1,680- $1,700To find the present value, use the formula:\[ PV = \frac{FV}{(1 + r)^n} \]Where:- $ PV $ is the present value- $ FV $ is the future value ($2,000)- $ r $ is the annual interest rate (3% or 0.03)- $ n $ is the number of years (6)Calculate to find the correct present value from the options provided.

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At 6% annual effective interest rate, how much money will be accumulated in 10 years for an initial investment of $1,000. The answer is most nearly: O $1,200 $1,400 $1,600 $1,800

FINANCIAL ACCOUNTING

10th Edition

ISBN:9781259964947

Author:Libby

Publisher:Libby

Chapter1: Financial Statements And Business Decisions

Section: Chapter Questions

Problem 1Q

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