On January 1, Alan King decided to transfer an amount from his checking account into an investment account that later will provide $97,000 to send his son to college (six years from now). The investment account will earn 8 percent, which will be added to the fund each year-end. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1) (Use appropriate factor (s) from the tables provided.) Required: How much must Alan deposit on January 1

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Brenton Powell

20 November, 00:56

On January 1, Alan King decided to transfer an amount from his checking account into an investment account that later will provide $97,000 to send his son to college (six years from now). The investment account will earn 8 percent, which will be added to the fund each year-end. (Future Value of $1, Present Value of $1, Future Value Annuity of $1, Present Value Annuity of $1) (Use appropriate factor (s) from the tables provided.) Required: How much must Alan deposit on January 1

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Khloe Mcclain · Answer 1

Alan should deposit $61126.45 today

Explanation:

The fact that the 8% interest on investment would be added to the initial investment each year signals that the question is on compound interest.

However, the amount that needs to be invested today is the present value of $97,000 discounted using the 8% interest rate and the timing horizon is 6 years.

PV=FV * (1+r) ^-n

FV is the amount expected in six years which is $97,000

r is the 8% rate of return or discount rate

n is the investment timing horizon which is six years.

PV=$97000 * (1+8%) ^-6

PV=$97,000 * (1.08) ^-6

PV=$97000*0.630169627

PV=$61126.45