9514 1404 393
Answer:
4.5765%
Step-by-step explanation:
Apparently, you have to figure out how long it would take to accumulate a balance of $10,457.65 with interest compounded, then use that time period to compute the equivalent simple interest rate. The relevant formulas are ...
A = P(1 +r/n)^(nt) . . . . amount of P at rate r compounded n times per year for t years
A = P(1 +rt) . . . . amount of P at rate r simple interest for t years
We need to use the first formula to find t, then use the second formula to find r. In both cases A=10457.65 and P=10000. Quarterly compounding means n=4. The interest rate is r=0.045 for the first formula.
Looking for t:
A/P = (1 +r/n)^(nt) . . . . . . . . . . divide by P
log(A/P) = nt·log(1 +r/n) . . . . . take logs
t = log(A/P)/(n·log(1 +r/n)) . . . divide by the coefficient of t
Filling in the given values, we find t to be ...
t = log(10457.65/10000)/(4·log(1 +0.045/4)) = 0.999998 ≈ 1.0
The compound interest is applied for 1 year (t=1), so now we can find r using the second formula.
A = P(1 +rt)
A/P -1 = rt
Filling in the known values, we have ...
1.045765 -1 = r = 0.045765 = 4.5765%
The equivalent simple interest rate on the deposit is 4.5765%.
