4)Jonathan invests $8,980 in a bank.  The bank pays 5.8% interest compounded quarterlya)How long must he leave the money in the bank for it to double? Round to nearest tenth of a year.  Show your work.b)How long will it take to triple? Round to nearest tenth of a year. Show your work.c)If Jonathan is given the choice to invest his money at 5.8% interest compounded quarterly for 5 years or invest his money compounding annually at a rate of 5.85% for 5 years, which option would be best for Jonathan? Explain and show your work.

Question
Asked Dec 2, 2019
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4)Jonathan invests $8,980 in a bank.  The bank pays 5.8% interest compounded quarterly

a)How long must he leave the money in the bank for it to double? Round to nearest tenth of a year.  Show your work.

b)How long will it take to triple? Round to nearest tenth of a year. Show your work.

c)If Jonathan is given the choice to invest his money at 5.8% interest compounded quarterly for 5 years or invest his money compounding annually at a rate of 5.85% for 5 years, which option would be best for Jonathan? Explain and show your work.

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Expert Answer

Step 1

(a)

Obtain the time taken to become the amount double as follows.

The time taken to become the amount double is given by A = 2P.

 

nt
A P 1
п
4t
5.8
2P P 1+
400
4t
5.8
log (2) log 1+
400
5.8
log 2 4r log 1
400
log 2
5.8
4log 1
400
t 12.0372 Years
t 12.04 (Round to nearest tenth)
Thus the time taken is t = 12 years
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Image Transcriptionclose

nt A P 1 п 4t 5.8 2P P 1+ 400 4t 5.8 log (2) log 1+ 400 5.8 log 2 4r log 1 400 log 2 5.8 4log 1 400 t 12.0372 Years t 12.04 (Round to nearest tenth) Thus the time taken is t = 12 years

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Step 2

(b)

Obtain the time taken to become the amount triple as follows.

The time taken to bec...

nt
A P 1
п
3P-r1
4t
5.8
ЗP P| 1+
400
4t
5.8
log (3) log 1
400
5.8
log (3) 4t log 1+
400
log (3)
5.8
4log 1
400
t =19.0758 Years
t 19.08 (Round to nearest tenth
Thus the time taken is t = 19 years
help_outline

Image Transcriptionclose

nt A P 1 п 3P-r1 4t 5.8 ЗP P| 1+ 400 4t 5.8 log (3) log 1 400 5.8 log (3) 4t log 1+ 400 log (3) 5.8 4log 1 400 t =19.0758 Years t 19.08 (Round to nearest tenth Thus the time taken is t = 19 years

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