MATH SOLVE

3 months ago

Q:
# An account is opened with an initial deposit of $7,500 and earns 3.6% interest compounded semi-annually for 30 years. How much more would the account have been worth if the interest were compounding weekly?

Accepted Solution

A:

Answer: He would have had more $192.288 if the interest were compounding weeklyStep-by-step explanation:Let us solve the problem in 2 stepsStep 1We would determine the amount compounded semi-annually for 30 years. Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500It was compounded semi-annually This means that it was compounded twice in a year. Son = 2The rate at which the principal was compounded is 3.6%. So r = 3.6/100 = 0.036It was compounded for a total of 30 years.n = 30The formula for compound interest is A = P(1+r/n)^ntWhereA = total amount in the account at the end of n years.A = 7500(1 + (0.036/2)^2Γ30A = 7500(1 + 0.018)^60A = 7500(1.018)^60A= $21873.987Step 2We would determine the amount compounded weekly for 30 years. Initial amount deposited into the account is $7,500. This means that the principal,P = $7,500It was compounded weekly. This means that it was compounded 52 times in a year. Son = 52The rate at which the principal was compounded is 3.6%. So r = 3.6/100 = 0.036It was compounded for a total of 30 years.n = 30Applying the formula for compound interest,A = P(1+r/n)^ntWhereA = total amount in the account at the end of n years.A = 7500(1 + (0.036/52)^52Γ30A = 7500(1 + 0.000692)^1560A = 7500(1.000692)^1560A = $22066.275Difference in amount = $22066.275 - $21873.987 = $192.288