Question

a)When your father was born 47 years ago, his grandparents deposited $175 in an account for him. Today, that account is worth $1,900. What was the annual rate of return on this account?

5.21 percent

5.00 percent

4.86 percent

3.89 percent

5.73 percent

1)Todd can afford to pay $390 per month for the next 7 years in order to purchase a new car. The interest rate is 6.8 percent compounded monthly. What is the most he can afford to pay for a new car today?

$26,008.50

$25,765.88

$24,708.07

$41,807.66

$26,875.45

2)Bob has been investing $7,500 in stock at the end of every year for the past 8 years. If the account is currently worth $93,400, what was his annual return on this investment?

3)You plan to save $390 per month starting today for the next 48 years "just to start the month off right." You feel that you can earn an interest rate of 9.5 percent compounded monthly. How much will there be in the account 48 years from today?

$4,151,522.47

$4,183,516.61

$3,791,344.72

$4,611,912.71

$4,575,688.51

Answer 1

Answer a.

Amount Deposited = $175
Period = 47 years
Accumulated Sum = $1,900

Let annual rate of return be i%

Accumulated Sum = Amount Deposited * (1 + Interest rate)^Period
$1,900 = $175 * (1+ i)^47
10.85714 = (1+ i)^47
1 + i = 1.0521
i = 0.0521 or 5.21%

So, annual rate of return is 5.21%

Answer 1.

Monthly Payment = $390
Period = 7 years or 84 months
Annual Interest rate = 6.8%
Monthly Interest rate = 0.5667%

Cost of Car = $390 * PVIFA(0.5667%, 84)
Cost of Car = $390 * (1 - (1/1.005667)^84) / 0.005667
Cost of Car = $390 * 66.68759
Cost of Car = $26,008.50

So, Todd can afford to purchase a car costing $26,008.50

Answer 2.

Annual Deposit = $7,500
Accumulated Sum = $93,400
Period = 8 years

Let annual rate of return be i%

$93,400 = $7,500 * PVIFA(i%, 8)
PVIFA(i%, 8) = 12.4533

Using financial calculator, i = 12.34%

So, annual return on this investment is 12.34%

Answer 3.

Monthly Deposit = $390
Period = 48 years or 576 months
Annual Interest Rate = 9.5%
Monthly Interest Rate = 9.5%/12
Monthly Interest Rate = 0.79167%

Accumulated Sum = $390*1.0079167^576 + $390*1.0079167^575 + $390*1.0079167^574 + ... + $390*1.0079167
Accumulated Sum = $390 * 1.0079167 * (1.0079167^576 - 1) / 0.0079167
Accumulated Sum = $4,611,912.71