Exam 9: Compound Interest: Further Topics and Applications

You are offered a loan at a rate of 10.5% compounded monthly. What would a semiannually compounded nominal rate have to be below to make it more attractive?

The amount owed on a promissory note for $950 after two years and five months is $1165.79. What monthly compounded nominal rate of interest was charged on the debt?

What was the annually compounded nominal rate of growth if the future value of $1000 after 20 years was $4016.94?

The Canadian Consumer Price Index (based on a value of 100 in 1971) rose from 97.2 in 1970 to 210.6 in 1980. What was the (equivalent) annual rate of inflation in the decade of the 1970s?

At what quarterly compounded nominal interest rate will money double in 75 months?

Calculate nominal rate of interest (to the nearest 0.01%):

Rounded to the nearest month, how long will it take a town's population to: a) Grow from 32,500 to 40,000 if the annual growth rate is 3%? b) Shrink from 40,000 to 32,500 if the annual rate of decline is 3%?

A credit union pays 5.25% compounded annually on five-year Compound Interest: Further Topics GICs. It wants to set the rates on its semiannually and monthly compounded GICs of the same maturity so that investors will earn the same total interest. What should be the rates on the GICs with the higher compounding frequencies?

ln[(1.03)⁴ (1.10)⁶] =

When he died in 1790, Benjamin Franklin left $4600 to the city of Boston, with the stipulation that the money and its earnings could not be used for 100 years. The bequest grew to $332,000 by 1890. What equivalent compound annual rate of return did the bequest earn?

What is the term of a compound-interest Guaranteed Investment Certificate if $8,500 invested at 6.1% compounded annually will earn interest totalling $4,365.50?

Calculate the missing interest rate (to the nearest 0.01%)

A trust company pays 5.5% compounded semiannually on its three-year GICs. For you to prefer an annually compounded GIC of the same maturity, what value must its nominal interest rate exceed?

Calculate the effective annual rate for 18% compounded annually.

Calculate the effective annual rate if $100 grew to $165 in 11.5 years with quarterly compounding.

Calculate nominal rate of interest (to the nearest 0.01%):

The insurance premium on a building is 0.05% of the face value. The face value is 75% of the building's market value. The insurance premium is $1650. What is the face value of the policy?

Which investment scenario requires more time: "$1 growing to $2" or "$3 growing to $5"? Both investments earn the same rate of return. Justify your choice.

In June of 2006, AIC Limited published full-page advertisements focused on the fact that its AIC Advantage Mutual Fund was Canada's "Best Performing Canadian Equity Fund over the 20 years" ending May 31, 2006. The equivalent annual rate of return during the 20 years was 11.9% compared to 9.9% for the benchmark S&P/TSX Composite Total Return Index. But the advertisement failed to point out that during the second half of that 20-year period, the fund's 9.4% compounded annual return was actually less than the 10.2% growth rate for the S&P/TSX Composite Total Return Index. Furthermore, in the final 5 years of the 20-year period, the fund's 2.4% annual rate of return was far below the index's 9.5% annual growth. The Advantage Fund's five-year performance was even less than the median performance of all Canadian equity mutual funds. In short, AIC was still trying to capitalize on the initial 10 years of truly outstanding performance, even though the Advantage Fund's subsequent 10 years' performance was at best mediocre. a) What would $10,000 invested in the AIC Advantage Fund on May 31, 1986 have grown to after 20 years? b) What was this investment worth after the first 10 years? c) What compound annual rate of return did the AIC Advantage Fund earn during the first 10 years of the 20-year period? d) What was the overall percent increase in the value of an investment in the AIC Advantage Fund during: (i) The first 10 years? (ii) The second 10 years?

A bank pays a simple interest rate of 4.1% on 30 to 179-day GICs of at least $100,000. What is the effective annualized rate of return: a) On a 40-day GIC? b) On a 160-day GIC?