Question

"Shekhar invests $1,820 in a mutual fund at the end of each of the next six years. If his opportunity cost rate is 8 percent compounded annually, how much will his investment be worth after the last annuity payment is made?"

Answer 1

The question asks for the future value of a series of annuity payments made by Shekhar at an 8% compounded annual rate. Using the future value of an annuity formula, one can calculate the total amount of Shekhar's investment after the last annuity payment is made.

Step-by-step explanation:

The student's question involves calculating the future value of a series of annuity payments using the compound interest formula. Specifically, Shekhar invests $1,820 annually in a mutual fund at an opportunity cost rate of 8% compounded annually for six years. To find the total amount of the investment after the last payment, one would use the future value of an annuity formula:

FV = Pmt × {((1 + r)^n - 1) / r}

Where FV is the future value of the annuity, Pmt is the annual payment, r is the annual interest rate, and n is the number of payments. In this problem, Pmt would be $1,820, r would be 0.08 (8%), and n would be 6. By plugging these values into the formula, we could calculate the future value of Shekhar's investment immediately after the last payment. It's important to mention this kind of calculation is crucial for planning savings and understanding the benefits of compound interest over time.

Answer 2

The investment will have a value of $2875.60 after 6 years.

Step-by-step explanation:

The formula to determine the final value of this investment at the end of this period is:

Future Value= Present Value*(1+r)^n

Where:

Present Value= Current value is capital today. In this case $1,820

Future Value= It is the value that is generated as a result of a compound nominal rate applied to a certain number of periods in which said rate is applied plus the present value.

r= The interest rate at which the debt is generated is determined in percentage and its duration is annual. In this case 8%

n=The periods that the investment or debt will last. In this case there are 6 periods because the investment is annual.

FV= 1820 *(1+0.08)^6

FV=1820*1.58

FV= 2875.60