Question

A. The value of an asset worth $18,000 today has appreciated at a constant rate of 2.4% compounded monthly. What was the asset worth 30 years ago?

B. What amount invested 11 years ago at 8.4% compounded monthly would generate $550 today?

C. Jorge deposited money 16 years ago in an account earning 3% interest compounded semiannually. He now has $60,000 in the account. What lump sum amount did he originally deposit 16 years ago?

D. If money can earn 6% interest compounded monthly, the investment of what amount 3 years ago would result in a total of $3,000 today?

Please explain clearly :)

Answer 1

=> All these questions can be solved by using the compound interest formula:

, where A is the final amount , P is the principal , r is the interest rate , n is number of times compounded in a time period and t is the time period.

A) The value of an asset worth $18,000 today has appreciated at a constant rate of 2.4% compounded monthly. What was the asset worth 30 years ago?

=> Here, Final amount = $ 18,000 , Interest rate = 2.4% , number of times compounded = 12 (compounded monthly) , time period = 30 years and we have to find the value of the principal to get the asset worth 30 years ago

=> Plug those values into the formula

=> Therefore the asset worth $ 8,767.84 30 years ago

B) What amount invested 11 years ago at 8.4% compounded monthly would generate $550 today?

=> Here, Final amount = $ 550 , Interest rate = 8.4% , number of times compounded = 12 (compounded monthly) , time period = 11 years and we have to find the value of the principal to get the invested amount 11 years ago

=> Plug those values into the formula

=> Therefore the amount invested 11 years ago is $ 219.014

C) Jorge deposited money 16 years ago in an account earning 3% interest compounded semi annually. He now has $60,000 in the account. What lump sum amount did he originally deposit 16 years ago?

=> Here, Final amount = $ 60,000 , Interest rate = 3% , number of times compounded = 2 (compounded semi annually) , time period = 16 years and we have to find the value of the principal to get the deposited amount 16 years ago

=> Plug those values into the formula

=> Therefore the lump sum amount deposited 16 years ago is $ 37,259.58

D) If money can earn 6% interest compounded monthly, the investment of what amount 3 years ago would result in a total of $3,000 today?

=> Here, Final amount = $ 3,000 , Interest rate = 6% , number of times compounded = 12 (compounded monthly) , time period = 3 years and we have to find the value of the principal to get the invested amount 3 years ago

=> Plug those values into the formula

=> Therefore the invested amount 3 years ago is $ 2,506.93