(Annuity payments) Calvin Johnson has a 5000 debt balance on his Visa card that charges 12.9 percent APR compounded monthly. In
2 answers:
Answer:
42 months
Explanation:
To calculate the number months, we use ordinary annuity formula since that payment is expected to be made at the end of each month. The ordinary annuity formula is as follows:
PV = P × [{1 - [1 ÷ (1 + r)]^n} ÷ r] .............................. (1)
Where ,
PV = Present value of an annuity payment = $5,000
P = monthly payment = $150
r = interest rate = 12.9% annually = 0.129 annually = (0.129 ÷ 12) monthly = 0.01075 monthly
n = number of months = ?
Substituting the values into equation (1), we have:
5000 = 150 × [{1 - [1 ÷ (1 + 0.01075)]^n} ÷ 0.01075]
5000 ÷ 150 = {1 - [1 ÷ (1.01075)]^n} ÷ 0.01075
33.33 × 0.01075 = 1 - [1 ÷ (1.01075)]^n
1 - 0.36 = [1 ÷ (1.01075)]^n
0.64 = 1^n ÷ (1.01075)^n
Since 1^n = 1, we have:
0.64 = 1 ÷ (1.01075)^n
Rearranging, we have:
(1.01075)^n = 1 ÷ 0.64
(1.01075)^n = 1.56
By converting the exponential function to a logarithm function, we have:
n = log_{1.01075}1.56
n = 41.59 approximately 42 months.
Therefore, it will take Calvin Johnson 42 months to pay off his credit card.
You might be interested in
Answer:
The Coronavirus pandemic took the world by surprise and most people were not ready for the far reaching quarantine measures that were put in place. These measures along with the general fear of the disease meant that Consumers were demanding less of goods and services which had the effect of shifting the Short Run Demand curve to the left.
The world also saw travel restrictions put in place which were a serious blow to international commerce because suppliers found it hard to source goods. This reduced the supply of goods and services which also meant that the Short Run Aggregate Supply Curve shifted to the left as well.
The New Equilibrium led to a way lower output at Y¹ which is shows why GDP growth fell into negative.
As a result of decreased output and quarantine measures, companies could not afford to keep their employees and had to let go of a lot of them. This is why the Unemployment rate went up as well.
