Answer:
The amount needed to pay off the loan is $28,142
Step-by-step explanation:
We have to calculate the compound interest on the loan amount using the compound interest formula, and the time we will use will be 7 years, not 4 years, because the amount was compounded over 7 years, although it was paid in 4 years.
The formula is shown below;
[tex]A=P(1 + \frac{r}{n} )^{nt}[/tex]
where;
A = Future amount to be paid
P = Initial amount of loan borrowed
r = interest rate in ratio
n = number of compounding periods per year
t = number of years of compounding
∴ [tex]A=20,000(1 + \frac{0.05}{1} )^{(1*7)}[/tex]
= [tex]20,000(1.05)^{7}[/tex]
= $28,142
Answer:
The amount needed to pay off the loan = $28,142
Step-by-step explanation:
The question is based on compound interest, so the formula for calculating compound interest will be applied;
A = P(1 + r)^t
Where, A = The final amount
P = Initial Principal
r = Interest rate
t = time
The principal amount borrowed by the borrower = $20,000, rate, r = 5%. It was compounded annually for 7years, so time, t = 7. It is then required to find the total sum, the loan will amount to in seven years if it's compounded annually at 5% interest rate. This means that "A" is being sought after.
So, A = 20,000 × (1 + (5/100)^7
A = 20,000 × (1 + 0.05)^7
A = 20,000 × (1.05)^7
A = 20,000 × 1.4071
A = $28,142
Therefore, the loan will amount to $28,142 if it is compounded annually at the rate of 5% for 7 years.
So, even if the borrower of the loan is able to get the loan paid off earlier than agreed in the deal( for example, paid off in 4 years instead of 7 years as in the case of this borrower), he/she will nevertheless pay the complete sum, the loan was supposed to amount to over the period contained in the agreement/deal.
