Jonathan plans to start saving $4,000 per year and invest it in a mutual fund. She...

Jonathan plans to start saving $4,000 per year and invest it in a mutual fund. She plans to do this for the next 20 years. Jonathan then plans to add $5,000 per year for the next 20 years. Assume she earns 6% per year. Calculate his balance be at the end of the 40 years?

Solutions

Expert Solution

1. Value of $4000 annual savings at the end of year 20 = Amount * ( (1 + Interest)^n - 1) / r

Value of $4000 annual savings at the end of year 20 = 4000 * ( (1 + 0.06)^20 - 1) / 0.06

Value of $4000 annual savings at the end of year 20 = 4000 * 2.20713 / 0.06

Value of $4000 annual savings at the end of year 20 = $147142.36

2. Value of $147142.36 at the end of 40 years = Amount * (1 + Interest)^Years

Value of $147142.36 at the end of 40 years = 147142.36 * 1.06^20

Value of $147142.36 at the end of 40 years = 147142.36 * 3.2073

Value of $147142.36 at the end of 40 years = $471905.50

3.Value of $5000 annual savings at the end of year 20 = Amount * ( (1 + Interest)^n - 1) / r

Value of $5000 annual savings at the end of year 20 = 5000 * ( (1 + 0.06)^20 - 1) / 0.06

Value of $5000 annual savings at the end of year 20 = 5000 * 2.20713 / 0.06

Value of $5000 annual savings at the end of year 20 = $183927.96

4. Total value at the end of year 40 = $471905.50 + 183927.96

Total value at the end of year 40 = $655833.45

jeff jeffy answered 1 year ago

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