Financial Concepts and Application

Jayda will earn more interest in Year 2 than Clayton will earn.

This morning Clayton deposited $2,500 into an account that pays 5 percent interest, compounded annually. Also this morning, Jayda deposited $2,500 at 5 percent interest, compounded annually. Clayton will withdraw his interest earnings and spend it as soon as possible. Jayda will reinvest her interest earnings into her account. Given this information, which one of the following statements is true?

PV = $175,000/1.066^20 PV = $48,740.95

Twenty years from now, you hope to have $175,000 to buy a parcel of land. How much must you deposit as a lump sum today to achieve this goal at an interest rate of 6.6 percent, compounded annually?

$18,250 = $5,000 (1+r^15) r = 0.0901 or 9.01%

Fifteen years ago, you invested $5,000. Today, it is worth $18,250. What annually compounded rate of interest did you earn?

PV = $48,613.24/1.0405^28 PV = $15,994.70

Assume your mother invested a lump sum 28 years ago at 4.05 percent interest, compounded annually. Today, she gave you the proceeds of that investment, totaling $48,613.24. How much did your mother originally invest?

In today's dollars, Caroline's award is worth more than Jiexin's.

Caroline is going to receive an award of $20,000 six years from now. Jiexin is going to receive an award of $20,000 nine years from now. Which one of the following statements is correct if both individuals apply a discount rate of 7 percent?

FV = $50*(1.076^77) FV = $14,077.16

Claire's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much is the collection expected to be worth in 2025?

$235,000 = $50 [ (1+r)^117] r = 0.0749, or 7.49% FV = $235,000 (1.0749^20) FV = $997,000 (rounded to nearest 500)

In 1903 the winner of a competition was paid $50. In 2020, the winner's prize was $235,000. What will the winner's prize be in 2040 if the prize continues increasing at the same rate?

FV = $6,220 + ($6,220)*(0.11)*(40) FV = $33,588

Johathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years?

Sophia will have more money than Mallory.

Sophia and Mallory are the same age. At age 25, Sophia invests $6,000 at 7 percent, compounded annually. At age 30, Mallory invests $6,000 at 7 percent, compounded annually. All else constant, when they both reach age 60:

FV Simple = $6,500 + ($6,500) * (0.6) * (10) FV Simple = $10,400 FV Compound = $6,500*(1.06^10) FV Compound = $11,640.51 Difference: $11,640.51 - $10,400 = $1,240.51

You invested $6,500 at 6 percent simple interest. How much more could you have earned over a 10-year period if the interest had compounded annually?

increase

Your aunt has promised to give you $5,000 when you graduate from college. You expect to graduate three years from now. If you speed up your plans to enable you to graduate two years from now, the present value of the promised gift will:

He earned a lower interest rate than he expected.

Miles invested $5,000 ten years ago and expected to have $10,000 today. He has neither added nor withdrawn any money since his initial investment. All interest was reinvested and compounded annually. As it turns our, he only has $8,400 in his account today. Which one of the following statements must be true?

could have deposited less money today and still had $5,000 in four years in the account paid a higher rate of interest.

Nirav just opened a savings account paying 2 percent interest, compounded annually. After four years, the savings account will be worth $5,000. Assume there are no additional deposits or withdrawals. Given this information, Nirav:

$64,800 = $67,900*[1 + (-0.015)]^t t = 3.09 years

Oiaochu purchased a parcel of land costing $67,900. Today, that land is valued at $64,800. How long has she owned this land if the price has been decreasing by 1.5 percent per year?

$756 = $300 (1.045^t) t = 21 years Age today = 10+21 = 31 years

On your tenth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?