Question

An investor makes three deposits into a fund at the end of 2, 5, 7 years....

An investor makes three deposits into a fund at the end of 2, 5, 7 years. The amount of the deposit at time t is $150(1.025)t. Find the size of the fund at the end of 10 years, if the nominal rate of discount convertible quarterly is 0.07.

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Answer #1

Deposit in Year 2 =150*1.025*2 = $307.5

Deposit in Year 5 =150*1.025*5 = $768.75

Deposit in Year 7 =150*1.025*7 = $1076.25

Annual Discount Rate =0.07 compounded quarterly

Effective discount rate = (1+i)^n-1=(1+0.07/4)^4-1=(1+0.0175)^4-1 = 1.0175^4-1 = 1.07186-1=0.07186

Future value of year 2 deposit will compound for 10-2=8 years. Hence FV = 307.5*(1+0.07186)^8 = 307.5*1.7422=$535.73

Future value of year 5 deposit will compound for 10-5=5 years. Hence FV = 768.75*(1+0.07186)^5 = 768.75*1.4148=$1087.61

Future value of year 7 deposit will compound for 10-7=3 years. Hence FV = 1076.25*(1+0.07186)^3 = 1076.25*1.2314=$1325.34

Total FV = 535.73+1087.61+1325.34= $2948.68

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