To determine how much more needs to be deposited in order to have $600,000 in 5 years with a decrease in annual interest rate from 12% to 8% compounded semi-annually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount (amount initially deposited)
r = the annual interest rate (as a decimal)
n = the number of compounding periods per year
t = the number of years
For the initial interest rate of 12%, substituting the given values into the formula:
600,000 = P(1 + 0.12/2)^(2*5)
600,000 = P(1 + 0.06)^10
600,000 = P(1.06)^10
Now, for the decreased interest rate of 8%, we'll use the same formula:
600,000 = P(1 + 0.08/2)^(2*5)
600,000 = P(1 + 0.04)^10
600,000 = P(1.04)^10
To find the difference in the principal amounts, we can divide the two equations:
(P(1.06)^10) / (P(1.04)^10) = (1.06)^10 / (1.04)^10
Simplifying, we get:
(1.06)^10 / (1.04)^10 = 1.6399...
So, the amount 1.6399... times greater needs to be deposited to achieve the same future value of $600,000 with the decreased interest rate.
Multiplying the original deposit by 1.6399..., we can calculate how much more needs to be deposited:
Additional deposit = P * 1.6399...
Note: Without knowing the specific initial deposit amount, we cannot calculate the exact additional amount required.
If annual interest rate falls from 12 to 8% per annum, how much more be deposited in an account to have 600000 in 5 years if both rates are compounded at semi annually?
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