What would $400.43 be worth if you invested it at 1% real interest for 47 years?

Question

What would $400.43 be worth if you invested it at 1% real interest for 47 years?

If, instead, you deposited $5 in a bank at 1% real interest, how much would you have at the end of the first year?

If you did this every year for 47 years, how much would you have at age 65?

If you earned 5% real interest on your deposits, how much would you have at age 65?

Which option would make you better off at age 65? How many times better off?

What would $400.43 be worth if you invested it at 1% real interest for 47 years?

If, instead, you deposited $5 in a bank at 1% real interest, how much would you have at the end of the first year?

If you did this every year for 47 years, how much would you have at age 65?

If you earned 5% real interest on your deposits, how much would you have at age 65?

Which option would make you better off at age 65? How many times better off?

Explanation / Answer

1. We have FV = PV*(1+r)^n = 400.43*(1+1%)^47 = $639.19 2. FV = PV*(1+r)^n = 5*(1+1%)^1 = $5.05 3. If you deposit $5 every year for 47 Yrs at 1%, we will calculta ethe FV of annuity of PMT=$5, nper = 47, Rate =1% SO FV of annuity = AMt at Age 47 = FV(Rate,nper,PMT) = FV(1%,47,-5) = $298.13 Now this amount will remain invested till age 65 ie (65-47 = 18 yrs) at 1% So AMount at Age 65 = FV = PV*(1+r)^n = $298.13*(1+1%)^18 = $356.61 4. If Rate is 5% in 3 above, how much I will have at age 65. If you deposit $5 every year for 47 Yrs at 5%, we will calculta ethe FV of annuity of PMT=$5, nper = 47, Rate =5% SO FV of annuity = AMt at Age 47 = FV(Rate,nper,PMT) = FV(5%,47,-5) =$890.60 Now this amount will remain invested till age 65 ie (65-47 = 18 yrs) at 5% So AMount at Age 65 = FV = PV*(1+r)^n = $890.60 *(1+5%)^18 = $2,143.34 5. Option 4 is better

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