Josh's grandparents established a college fund for him when he was born. They deposited $8,200 into an account that earned 9.88% interest. Assuming Josh goes to college at age 18, how much money will he have if...
a) ... the interest is calculated only once during the entire loan?
b) ... the interest is compounded weekly?
a) 8200 × 0.0988 × 18 = $14582.88
8200 + 14582.88 =
$22782.88 -correct
b) 8200(1.0019)^936 =
$48,465.24 -correct
a) If the interest is calculated only once during the entire loan, we can calculate the amount Josh will have using the simple interest formula:
Simple Interest = Principal × Interest Rate × Time
The principal amount deposited for Josh is $8,200, the interest rate is 9.88%, and the time is the period between when Josh was born and when he goes to college at age 18, which is 18 years.
Simple Interest = $8,200 × 0.0988 × 18
Simple Interest = $14,464.08
Therefore, Josh will have a total of $14,464.08 in his college fund if the interest is calculated only once during the entire loan.
b) If the interest is compounded weekly, we can calculate the amount Josh will have using the compound interest formula:
Compound Interest = Principal × (1 + Interest Rate / Number of Compounding Periods)^(Number of Compounding Periods × Time)
In this case, the interest rate is 9.88%, and the time is still 18 years. However, we need to convert the interest rate to its equivalent weekly interest rate. There are 52 weeks in a year, so the weekly interest rate would be 9.88% / 52 = 0.1896%.
Using this weekly interest rate, we can calculate the compound interest:
Compound Interest = $8,200 × (1 + 0.001896)^ (52 × 18)
Compound Interest = $8,200 × (1.001896)^936
Compound Interest = $31,438.24
Therefore, Josh will have a total of $31,438.24 in his college fund if the interest is compounded weekly.
a) To calculate the amount Josh will have if the interest is calculated only once during the entire loan, we can use the formula for simple interest:
A = P + (P * r * t)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = interest rate
t = time (in years)
Given that the initial deposit (P) is $8,200, the interest rate (r) is 9.88% (which can be written as 0.0988 as a decimal), and the time (t) is 18 years, we can substitute these values into the formula to find the final amount (A):
A = 8,200 + (8,200 * 0.0988 * 18)
A = 8,200 + 14,455.04
A ≈ $22,655.04
Therefore, if the interest is calculated only once during the entire loan, Josh will have approximately $22,655.04 for college.
b) To calculate the amount Josh will have if the interest is compounded weekly, we can use the formula for compound interest:
A = P * (1 + (r / n))^(n * t)
Where:
A = the final amount
P = the principal amount (initial deposit)
r = interest rate
n = number of compounding periods per year
t = time (in years)
Given that the initial deposit (P) is $8,200, the interest rate (r) is 9.88% (which can be written as 0.0988 as a decimal), the number of compounding periods per year (n) is 52 (as there are 52 weeks in a year), and the time (t) is 18 years, we can substitute these values into the formula to find the final amount (A):
A = 8,200 * (1 + (0.0988 / 52))^(52 * 18)
A ≈ 8,200 * (1 + 0.0018979)^(936)
A ≈ 8,200 * (1.0018979)^936
A ≈ 8,200 * 3.6233
A ≈ $29,711.06
Therefore, if the interest is compounded weekly, Josh will have approximately $29,711.06 for college.
a) ridiculous question ! , makes no sense
the "arithmetic" would be 8200(1.0988) = ....
b)
weekly rate = .0988/52 = .0019
number of weeks in 18 years = 936
amount = 8200(1.0019)^936 = $48,465.24