Question

Suppose you borrow $25,000 at an interest rate of 6.2% compounded monthly. If your monthly payment is $231.49.

Answer 1

Answer:

Balance of the loan at the end of 2 months = $252357.32

Step-by-step explanation:

Principal = $25000

Interest = 6.2% , Monthly Payment = 231.49

n = number of times the interest is compounded in a year

⇒ n = 1 ( because it is mentioned the rate is compounded is monthly )

Time = 1 month = 0.083 years

Balance of the loan at the end of one month :

$Amount=P\cdot (1+\frac{rate}{n})^{n\cdot t}\\\\Amount=25000\cdot (1+\frac{6.2}{100\times 12})^{12\times \frac{1}{12}}\\\\\implies Amount =\ 251291.67$

Balance of the loan at the end of two months :

Now after monthly payment of $239.31, the Principal becomes :

Principal = Amount after one month - Monthly Payment

              = 251291.67 - 231.49

              = $ 251060.18

$Amount=P\cdot (1+\frac{rate}{n})^{n\cdot t}\\\\Amount=251060.18\cdot (1+\frac{6.2}{100\times 12})^{12\times \frac{1}{12}}\\\\\implies Amount =\ 252357.32$

Hence , Balance of the loan at the end of 2 months = $252357.32