2 points 11 what is the future value of$3200 invested at 8% years compounded qua

Question

2 points 11 what is the future value of$3200 invested at 8% years compounded quarterly for 3 2 points 12. How long will it take an investment of $5000 to grow to $6000 5% interest compounded quarterly. if it is invested at 2 points 13 What is the future value of $1400 invested at 8% compounded continuously for 12 years 2 points 14. Suppose that $800 is deposited at the end of every 6-month period for 10 years in an account that pays 12%, compounded semiannually. Find the future value of the annuity 2 points 15. Find the lump sum that one must invest in an annuity in order to receive $10000 semi-annually for the next 10 years, if the annuity pays 9%, compounded semiannually

Explanation / Answer

Answer 11.

Amount Invested = $3,200
Annual Interest Rate = 8%
Quarterly Interest Rate = 8%/4 = 2%
Time Period = 12 (3 years)

Future Value = $3,200 * 1.02^12
Future Value = $4,058.37

Answer 12.

Amount Invested = $5,000
Accumulated Sum = $6,000
Annual Interest Rate = 5%
Quarterly Interest Rate = 5%/4 = 1.25%

Let n be the number of quarters in which $5,000 will grow to $6,000

$6,000 = $5,000 * 1.0125^n
1.2 = 1.0125^n
n = ln (1.2) / ln(1.0125)
n = 14.68 quarter

Number of years = 14.68 / 4
Number of years = 3.67 years

Answer 13.

Amount Invested = $1,400
Annual Interest Rate = 8%
Time Period = 12 years

Future Value = $1,400 * e^(0.08 * 12)
Future Value = $1,400 * 2.611696
Future Value = $3,656.38

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