Mastering Simple Interest and Future Value Calculations
1. Avril's Bank Deposit
Avril deposited $800 in his bank at 1.5% for five years. Let's calculate the amount of interest Avril will earn using the simple interest formula:
Simple Interest Formula: Interest = Principal × Rate × Time
Interest = $800 × 1.5% × 5 = $60
Now, let's calculate the future value of Avril's deposit:
Future Value = Principal + Interest = $800 + $60 = $860
2. Phyllis' Loan
Phyllis borrowed $1,000 at 2% APR for six months. If she pays $200 two months into the loan and the rest at six months, let's calculate the total amount of interest Phyllis will pay using the simple interest formula:
Interest = Principal × Rate × Time
Interest = $1,000 × 2% × 6/12 = $10
Therefore, Phyllis will pay a total of $10 in interest.
3. James' Bank Deposit
James deposited $500 in his bank at 4.5% for 90 days. Let's calculate the amount of interest James will earn using exact interest:
Exact Interest = Principal × Rate × Time
Exact Interest = $500 × 4.5% × 90/365 = $5.48
Now, let's calculate the future value of James' deposit:
Future Value = Principal + Interest = $500 + $5.48 = $505.48
4. Ariel's Discount Note
Ariel signed a simple discount note for $3,500 at 3 1/2% for 60 days. Let's calculate the amount of interest Ariel will pay using ordinary interest:
Interest = Principal × Rate × Time
Interest = $3,500 × 3.5% × 60/360 = $19.38
Now, let's calculate the proceeds Ariel will receive on May 4:
Proceeds = Principal - Interest = $3,500 - $19.38 = $3,480.62
Amount to pay at maturity = Principal = $3,500
The note will be due on July 3.
5. APY for 16% APR
The effective rate (APY) for 16% APR compounded quarterly is:
APY = (1 + r/n)^n - 1
APY = (1 + 0.16/4)^4 - 1 = 16.36%
6. Louisa's Investment
Louisa invested $4,500 at 4% interest compounded semiannually for two years. Let's calculate the future value of Louisa's investment:
Future Value = Principal × (1 + Rate)^Time
Future Value = $4,500 × (1 + 0.04)^4 = $4,912.08
7. Cleve's Deposit
Cleve wants to have $8,000 in five years at a rate of 6% compounded quarterly. Let's calculate the amount he needs to deposit now:
Principal = Future Value / (1 + Rate)^Time
Principal = $8,000 / (1 + 0.06)^20 = $5,342.42
8. Payday Loan
If you want to borrow $900 for 20 days, the dollar amount of interest is:
Interest = Principal × Rate × Time
Interest = $900 × 12/100 × 20/365 = $5.92
Therefore, the APR of this loan is 292.54%.
9. Future Value of an Ordinary Annuity
The future value of an annuity with a quarterly payment of $1,000 for four years compounding quarterly at 8% is:
Future Value = Payment × [(1 + Rate/n)^nt - 1] / (Rate/n)
Future Value = $1,000 × [(1 + 0.08/4)^(4*4) - 1] / (0.08/4) = $20,439.90
10. Future Value of an Annuity Due
The future value of an annuity due with a monthly payment of $50 for 2.5 years compounding monthly at 6% is:
Future Value = Payment × [(1 + Rate/n)^nt - 1] / (Rate/n) × (1 + Rate/n)
Future Value = $50 × [(1 + 0.06/12)^(12*2.5) - 1] / (0.06/12) × (1 + 0.06/12) = $1,406.45
Questions:
1. What is the total amount of interest Phyllis will pay for her loan?
2. When will Ariel's discount note be due?
3. What is the APY for 16% APR compounded quarterly?
Answers:
1. Phyllis will pay a total of $10 in interest for her loan.
2. Ariel's discount note will be due on July 3.
3. The APY for 16% APR compounded quarterly is 16.36%.