To calculate the future value of a monthly bank deposit, we can use the formula:
FV = P * ((1 + r)^nt - 1) / r
Where:
FV = Future Value
P = Monthly deposit
r = Interest rate per period (monthly in this case)
n = Number of periods (in this case, the number of months)
t = Time in years
In this case, we know:
P = $100
r = 5% = 0.05 (monthly interest rate)
n = 10 years = 10 * 12 = 120 months
Substituting the values into the formula:
15,528.23 = 100 * ((1 + 0.05)^(120) - 1) / 0.05
Solving for (1 + 0.05)^(120) - 1:
(1 + 0.05)^(120) - 1 = 155.2823
We can now rewrite the equation:
15,528.23 = 100 * 155.2823 / 0.05
Simplifying:
15,528.23 = 100 * 3,105.646
Dividing both sides by 100:
155.2823 = 3,105.646
Therefore, expressing 15,528.23 in scientific notation:
15,528.23 = 1.552823 × 10^4
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.
1 answer
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