Question

Anna barrowed 20000 at 5% for three and a half years. She wants to pay 8000 on maturity. To achieve this, she has to pay 2000 in 10 months, and 5000 in 16 months from now. How much should she pay in two and a half years from now to meet her obligation?​

Answer 1

$8980

Step-by-step explanation:

First, let's calculate the total interest Anna will pay over the three and a half years:

Interest = Principal x Rate x Time

Interest = 20000 x 0.05 x 3.5

Interest = 3500

So, Anna will have to pay back the principal amount of 20000 plus the interest of 3500, which equals 23500.

Next, let's calculate how much Anna will have paid back by the time she makes her first payment of 2000 in 10 months:

Interest for 10 months = 20000 x 0.05 x (10/12) = 833.33

Amount paid towards principal = 2000 - 833.33 = 1166.67

Remaining balance = 20000 - 1166.67 = 18833.33

Now, let's calculate how much Anna will owe at the time of her second payment of 5000 in 16 months:

Interest for 16 months = 18833.33 x 0.05 x (16/12) = 1255.56

Amount paid towards principal = 5000 - 1255.56 = 3744.44

Remaining balance = 18833.33 - 3744.44 = 15088.89

Finally, we can calculate how much Anna will owe in two and a half years from now:

Interest for 30 months = 15088.89 x 0.05 x (30/12) = 1891.11

Amount paid towards principal = remaining balance + interest - final payment

Amount paid towards principal = 15088.89 + 1891.11 - 8000 = 8980

Therefore, Anna should pay $8980 in two and a half years from now to meet her obligation.

Answer 2

Step-by-step explanation:

Principal amount = $20,000

Interest rate = 5%

Time = 3.5 years

Using the formula for simple interest:

Interest = (Principal x Rate x Time) / 100

Interest = (20000 x 5 x 3.5) / 100

Interest = $3,500

Total amount owed = Principal + Interest

Total amount owed = $20,000 + $3,500

Total amount owed = $23,500

Anna wants to pay $8,000 on maturity, which means she still owes:

Remaining amount = Total amount owed - Payment on maturity

Remaining amount = $23,500 - $8,000

Remaining amount = $15,500

Anna has to pay $2,000 in 10 months, which means she still owes:

Remaining amount = Remaining amount - $2,000

Remaining amount = $15,500 - $2,000

Remaining amount = $13,500

Anna has to pay $5,000 in 16 months, which means she still owes:

Remaining amount = Remaining amount - $5,000

Remaining amount = $13,500 - $5,000

Remaining amount = $8,500

Now Anna has to find out how much she should pay in 2.5 years to meet her obligations.

Time = 2.5 years

Using the formula for simple interest:

Interest = (Principal x Rate x Time) / 100

Interest = (8500 x 5 x 2.5) / 100

Interest = $1,062.50

Total amount owed after 2.5 years = Principal + Interest

Total amount owed after 2.5 years = $8,500 + $1,062.50

Total amount owed after 2.5 years = $9,562.50

To meet her obligations, Anna needs to pay:

Remaining amount = Total amount owed after 2.5 years - Payments made so far

Remaining amount = $9,562.50 - $8,000 - $2,000 - $5,000

Remaining amount = $562.50

Therefore, Anna needs to pay $562.50 in 2.5 years from now to meet her obligations.