Mary is 30 years old and has a retirement account with a current balance of $50,
ID: 2755190 • Letter: M
Question
Mary is 30 years old and has a retirement account with a current balance of $50,000. Mary wants to retire at age 60. What interest rate would need to be earned in order to accumulate a total of $1,000,000 in 30 years, by adding $6,000 annually Mary is 30 years old. What is the present value of her trust fund if it promises to pay her $50,000 on her 37th birthday (7 years from today) and earns 10% compounded annually Mary is looking at buying a new car: How much must Mary deposit today in an account earning 6% annually to accumulate a 20% downpayment to use in purchasing a car one year from now, assuming that the car's current price is $20,000 and inflation will be 4%Explanation / Answer
1) Calculate the interest rate:
The following spread sheet calculates the interest rate using the rate function in excel:
Thus, the interest rate which is required to earn is 7.24%
2) Calculate the present value:
The formula for calculating the present value is as follows:
PV = FV / (1+i)n
Substitute:
PV = $50,000 / (1+0.01)7
= $25,657.91
Thus, the present value is $25,657.91
3)Calculate the present value:
The formula to calculate the future value is as follows:
FV = { Current price + (Current price *nInflation)} * Down payment
Substitute:
FV = { $20,000 + ($20000*4%)}*20%
=$ 20,800 * 0.02
= $ 4,160
Thus, the Future value is $4,160
To calculate the present value the formula is as follows:
PV = FV / (1+i)n
Substitute:
PV = $4,160 / (1+0.06)1
= $3,924.55
Thus, the present value is $3,924.55
PV $50,000 PMT $6,000 FV ($1,000,000) n $30 r 7.24%