Bob took out a bank loan for 60 000 that must be repaid with regular monthly payments of $1000. The bank charges him an interest rate of 3.0% compounded monthly. How many payments will Bob have to make to pay off the loan?
a) 70 b) 59 c) 72 d) 66
I got B (59) is that right?
no
show me your work so I can tell you where you went wrong.
I just added in the numbers to the formula and 59 just appeared so i just assumed that was it lol
That's what I used to call mathemagics
- unfortunately you are wrong!
"I just added in the numbers to the formula and 59 just appeared" ---- nonsense!
What formula? Show me if you want help
thats why im asking you for help because idk mate
Again, what formula are you using ??
TVM solver
To determine the number of payments Bob needs to make to pay off the loan, we can use the formula for calculating the number of periods (payments) required to pay off a loan with a fixed payment amount and interest rate. The formula is derived from the future value of an ordinary annuity.
The formula for calculating the number of payments is:
n = -log(1 - r(PV) / PMT) / log(1 + r)
Where:
n = number of payments
r = interest rate per period (monthly rate in this case)
PV = present value or loan amount
PMT = monthly payment
Let's plug in the values from the given information into the formula:
PV = $60,000
PMT = $1,000
r = 3.0% / 100 = 0.03 (monthly rate)
n = -log(1 - 0.03 * 60,000 / 1,000) / log(1 + 0.03)
Let's calculate this using a calculator or a spreadsheet:
n ≈ 59.17
Since we can't have fractional payments, we need to round up the number of payments to the nearest whole number. Hence, Bob will have to make 59 payments to pay off the loan.
Thus, the correct answer is option b) 59.