MAT 1460 Homework Section 52 Support your answer by showing

MAT 1460- Homework Section 5.2 Support your answer by showing your work Jennifer has a balance of $1500 on her credit card that she is unable to pay for a 30 days. 2. Austin\'s grandparents wish to createa savings account paying 4.8% annual interest compounded monthly on the day of his birth. How much money would they need to deposit now so that there would be $10,000 in the account on his 18th birthday? Round your answer to the nearest dollar. 1. Assuming that the credit card company charges an annual interest rate of 19.95% compounded daily, what is the amount of interest that she will be charged? Assumed a 360-day year and round your answer to the nearest cent. 3. How long would you need to leave $100 in a 4. Marisa find two accounts the savings account paying 2.4% annual interest compounded monthly so that there would be $1,000,000 in the account? Round your answer to the nearest month. following interest rates: Country Bank at 4.85% compounded quarterly and Pool Bank at 4.825% compounded monthly. Find the effective rate (APY) for each account and determine which has the higher nominal rate. |

Solution

1.

Number of monthly compounding period in 18 years = n = 18 years * 12 = 216

Monthly interest rate = r = 4.8%/12 = 0.4% = 0.004

Future value = $10,000

Future value of deposit = Amount of deposit * (1+r)ⁿ

$10,000 = Amount of deposit*1.004²¹⁶

$10,000 = Amount of deposit * 2.36855

Amount of deposit = $10,000/2.36855 = $4,221.99

2.

Amount of credit = $1,500

Days of default = n = 30

Daily interest rate = 19.95%/360 = 0.055417% = 0.00055417

Amount to be paid after 30 days = $1,500*1.00055417³⁰ = $1,525.14

Interest to be charged = $1,525.14 - $1,500 = $25.14

3.

Amount of deposit = $100

Future value = $1,000,000

Monthly interest rate = r = 2.4%/12 = 0.2% = 0.002

Let the months of deposit be n

$1,000,000 = $100*1.002ⁿ

1.002ⁿ = $1,000,000/$100

1.002ⁿ = 10,000

n log 1.002 = log10000

n * 0.00086772 = 4

n = 4/0.00086772 = 4609.77

number of months = 4610

Number of years = 384

4.

Effective rate for country bank = (1 + 0.0485/4)⁴ – 1 = 0.0494 = 4.94%

Effective rate for Pool bank = (1 + 0.04825/12)¹² – 1 = 0.0493 = 4.93%

Country bank has higher nominal rate