Mike and Torri estimate that they want to buy a house for $158.000.00, and they need to make a down payment of 16,5% of the cost of their house. If they have 15 months to save for the down payment, how much do they need to invest into an account earning 3,431% compounded continuously so that they can reach their goal?

perlejatyh8

perlejatyh8

Answered question

2022-11-11

Mike and Torri estimate that they want to buy a house for $158.000.00, and they need to make a down payment of 16,5% of the cost of their house. If they have 15 months to save for the down payment, how much do they need to invest into an account earning 3,431% compounded continuously so that they can reach their goal?

Answer & Explanation

Ricardo Weiss

Ricardo Weiss

Beginner2022-11-12Added 12 answers

Answer:
Total amount of house=$158,000.
Amount of down payment=16.5% of total amount
= 16.5 %  of  158 , 000 = ( 158 , 000 16.5 ) / 100 = 1580 16.5 = $ 26070
Rate of interest r = 3.431 %
Time span=15months=15/12years=1.25years.
Formula:
Total amount after 'n' years is,when compounded continuosly
A = P ( 1 + ( r 100 ) ) n
Where P is principal or initial investment, 'r' is rate of investment.
Now in present case total amount,A=26070
So by using above formula
26070 = P ( 1 + ( 3.431 100 ) ) 1.25 26070 = P ( 1 + 0.0341 ) 1.25 26070 = P ( 1.0341 ) 1.25 26070 = P 1.0427 P = 26070 1.0427 = $ 25002.40
so they should invest $25002.40 to get 16.6% down payment in 15 months.

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