Question
It takes 10 ears for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a × 10^(n) where a is single digit. _
Answers
GPT 3.5
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial deposit)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, a monthly deposit of $100 is made for 10 years at an interest rate of 5% compounded monthly.
P = $100
r = 5% = 0.05
n = 12 (monthly compounding)
t = 10
Plugging in these values into the formula, we get:
A = 100(1 + 0.05/12)^(12*10)
= 100(1 + 0.00416666667)^(120)
= 100(1.00416666667)^(120)
≈ 100(1.70973221311)
≈ 170.973221311
Rounding to the nearest place value, the amount is approximately $170.97.
Written in the form of a × 10^(n), where a is a single digit, $170.97 can be expressed as 1.7097 × 10^(2).
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal (initial deposit)
r = interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years
In this case, a monthly deposit of $100 is made for 10 years at an interest rate of 5% compounded monthly.
P = $100
r = 5% = 0.05
n = 12 (monthly compounding)
t = 10
Plugging in these values into the formula, we get:
A = 100(1 + 0.05/12)^(12*10)
= 100(1 + 0.00416666667)^(120)
= 100(1.00416666667)^(120)
≈ 100(1.70973221311)
≈ 170.973221311
Rounding to the nearest place value, the amount is approximately $170.97.
Written in the form of a × 10^(n), where a is a single digit, $170.97 can be expressed as 1.7097 × 10^(2).