Question

Alf needs to borrow $15,000 to pay for his college tuition. He can borrow the money from his parents at a rate of

3.55% interest compounded annually for 4 years, or he can borrow from his local bank at a rate of 3.50% interest
compounded continuously for 4 years.
Manipulation of Numerical Data
a) Use the information given to organize the data in the space provided below. For each option, write the formula
needed to use, list all variables from the formula, and assign a value to each variable. Do not perform any
calculations. What lead you to choose the formula for each option? Write your answer, with reasoning, in a
complete sentence with proper grammar and correct spelling.
Analysis of Numerical Data
b) Before performing any calculations, which option do you think will be the better loan for Alf? Write your answer,
with reasoning, in a complete sentence with proper grammar and correct spelling.
c. Calculate the total amount of money Alf will have to pay back for each option at the end of the 4 years. Show all
your work in the space provided below. Round your answer to the nearest cent.
d) Calculate the interest Alf will have to pay for each option at the end of the 4 years. Show all your work in the
space provided below. Round your answer to the nearest cent.

Answer 1

Comparing two loan options: one with annual compound interest and another with continuous compounding, using their respective formulas to show variables and reason for choice. Analysis suggests the continuously compounded loan might be higher despite a lower rate. Calculations would provide exact repayment amounts for each option.

Step-by-step explanation:

The student's question involves comparing two different loan options with differing interest rate structures and determining which would be the more economical choice over a 4-year period.

Manipulation of Numerical Data

For option A (parents' loan), the compound interest formula is P(1 + r/n)^(nt), where P is the principal amount ($15,000), r is the annual interest rate (0.0355), n is the number of times interest is compounded per year (1), and t is the time in years (4).

For option B (bank loan), the continuously compounded interest formula is Pe^(rt), where P is the principal amount ($15,000), r is the annual interest rate (0.035), and t is the time in years (4).

Analysis of Numerical Data

Prior to calculations, one might conjecture that the loan with continuous compounding could be higher due to the nature of continuous growth, even though the interest rate is slightly lower.

Calculation results

The exact calculations, based on the formulas provided, would yield the total amounts of money Alf would need to repay for each loan after 4 years.