Payments of $1800 and $2400 weere made on a $10,000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semi-annually for the first two years and 10.74% compounded monthly thereafter. What amount was owed on the loan after three years?

Question

Payments of $1800 and $2400 weere made on a $10,000 variable-rate loan 18 and 30 months after the date of the loan. The interest rate was 11.5% compounded semi-annually for the first two years and 10.74% compounded monthly thereafter. What amount was owed on the loan after three years?

Answer 1

I answered a similar question two days ago. See

http://www.jiskha.com/display.cgi?id=1249196489

Answer 2

To calculate the amount owed on the loan after three years, we need to determine the outstanding balance after 18 months, add the interest for the remaining 12 months, subtract the first payment of $1800, and then repeat the process for the remaining 12 months.

Let's break down the process step by step:

Step 1: Calculate the outstanding balance after 18 months.
To do this, we'll use the formula for compound interest:

Future Value = Principal * (1 + (Rate / Frequency))^ (Time * Frequency)

For the first 18 months:
Principal = $10,000
Rate = 11.5% (since it is compounded semi-annually)
Time = 18 months
Frequency = 2 (since it is compounded semi-annually)

Future Value = $10,000 * (1 + (0.115 / 2))^ (18 * 2)
Future Value = $10,000 * (1 + 0.0575)^ 36
Future Value = $10,000 * (1.0575)^ 36
Future Value after 18 months ≈ $11,358.06

Step 2: Add interest for the remaining 12 months.
To calculate the interest for 12 months, we'll use the same formula, but with the new interest rate and time:

Principal = $11,358.06 (the balance after 18 months)
Rate = 10.74% (since it is compounded monthly)
Time = 12 months
Frequency = 12 (since it is compounded monthly)

Future Value = $11,358.06 * (1 + (0.1074 / 12))^(12 * 1)
Future Value = $11,358.06 * (1 + 0.00895)^ 12
Future Value ≈ $12,480.77

Step 3: Subtract the first payment of $1800.
New Balance = $12,480.77 - $1800
New Balance ≈ $10,680.77

Step 4: Repeat steps 2 and 3 for the remaining 12 months and the second payment of $2400.

Principal = $10,680.77 (the new balance)
Rate = 10.74% (since it is compounded monthly)
Time = 12 months
Frequency = 12 (since it is compounded monthly)

Future Value = $10,680.77 * (1 + (0.1074 / 12))^(12 * 1)
Future Value ≈ $11,738.04

New Balance = $11,738.04 - $2400
New Balance ≈ $9,338.04

The amount owed on the loan after three years is approximately $9,338.04.