It takes 10 years 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.
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the final amount
- P is the principal amount (initial deposit)
- r is the annual interest rate (in decimal form)
- n is the number of times interest is compounded per year
- t is the number of years
In this case, our initial deposit P is $100, the annual interest rate r is 5% or 0.05, the number of times compounded per year n is 12 (monthly compounding), and the number of years t is 10.
Using the formula, we can plug in the known values:
A = 100(1 + 0.05/12)^(12*10)
≈ 100(1.0041666667)^(120)
≈ 100(1.647009)
≈ 164.7009
Rounding to the nearest penny, the amount is $164.70.
To express $15,528.23 in the form of (a×10^n):
The number $15,528.23 can be written as:
1.552823 × 10^4
Make A a single Digit
To make the value of A a single digit, we can divide it by the appropriate power of 10. In this case, we divide $15,528.23 by 10^4:
A = 15,528.23 / 10^4
= 1.552823
So, A can be expressed as 1.553.