Answer: So, you would need to pay approximately $164.04 each month to pay off the $5,000 credit card debt with a 19.9% interest rate in 3 years.
Explanation:
To calculate the monthly payment required to pay off a $5,000 credit card debt with a 19.9% interest rate in 3 years, you can use the formula for the monthly payment of a fixed-rate loan:
�
=
�
⋅
�
⋅
(
1
+
�
)
�
(
1
+
�
)
�
−
1
M=
(1+r)
n
−1
P⋅r⋅(1+r)
n
Where:
�
M is the monthly payment.
�
P is the principal amount (the credit card debt, $5,000 in your case).
�
r is the monthly interest rate (annual interest rate divided by 12 months and converted to a decimal form).
�
n is the total number of payments (monthly payments for 3 years, which is
3
×
12
=
36
3×12=36 months).
Let's calculate it step by step:
Convert the annual interest rate to a monthly rate:
�
=
19.9
%
12
×
100
=
0.016583
r=
12×100
19.9%
=0.016583
Calculate the total number of payments:
�
=
3
×
12
=
36
n=3×12=36 months.
Now, plug these values into the formula:
�
=
5
,
000
⋅
0.016583
⋅
(
1
+
0.016583
)
36
(
1
+
0.016583
)
36
−
1
M=
(1+0.016583)
36
−1
5,000⋅0.016583⋅(1+0.016583)
36
Calculate the numerator first:
�
�
�
�
�
�
�
�
�
=
5
,
000
⋅
0.016583
⋅
(
1
+
0.016583
)
36
Numerator=5,000⋅0.016583⋅(1+0.016583)
36
Calculate the denominator:
�
�
�
�
�
�
�
�
�
�
�
=
(
1
+
0.016583
)
36
−
1
Denominator=(1+0.016583)
36
−1
Now, calculate the monthly payment:
�
=
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
M=
Denominator
Numerator
Using a calculator, you can find the approximate value of
�
M. It will be approximately:
�
≈
5
,
000
⋅
0.016583
⋅
2.01265468202
2.01265468202
−
1
≈
166.058175
1.01265468202
≈
164.04
M≈
2.01265468202−1
5,000⋅0.016583⋅2.01265468202
≈
1.01265468202
166.058175
≈164.04
So, you would need to pay approximately $164.04 each month to pay off the $5,000 credit card debt with a 19.9% interest rate in 3 years.